





I 


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SUMMARY TECHNICAL REPORT 
OF THE 

NATIONAL DEFENSE RESEARCH COMMITTEE 


DECLASSIFIED 
By authority Secretary of 

OCT ly 1960 


Defense memo 2 August 1960 


LIBRARY OF CONGRESS 



and Nav’ 


of any material. 


^oljpMWttfT^ may 
^reader is advised to consult the War 
H the reverse of this page for the current classification 


tr TiurTTLATION: BEFORE SERVICING 
uSkOS must _D«AN2IXKD. 


■3 

T^y.CLASSIFIE D 
By authority Secretary of 


0C1 1 h 196U 


V' 


PefeDse memo 2 August 1960 

t ,-ttiTI ARY of congress 


”anuscript and illustrations for this volume were prepared for 
publication by the Summary Reports Group of the Columbia 
University Division of War Research under contract OEMsr-1131 
with the Office of Scientific Research and Development. This vol- 
ume was printed and bound by the Columbia University Press. 


Distribution of the Summary Technical Report of NDRC has been 
made by the War and Navy Departments. Inquiries concerning the 
availability and distribution of the Summary Technical Report 
volumes and microfilmed and other reference material should be 
addressed to the War Department Library, Room lA-522, The 
Pentagon, Washington 25, D. C., or to the Office of Naval Research, 
Navy Department, Attention: Reports and Documents Section, 
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2 


d his volume, like the seventy others of the Summary Technical 
Report of NDRC, has been written, edited, and printed under 
great pressure. Inevitably there are errors which have slipped past 
Division readers and proofreaders. There may be errors of fact not 
known at time of printing. The author has not been able to follow 
through his writing to the final page proof. 


Please report errors to: 


JOINT RESEARCH AND DEVELOPMENT BOARD 
PROGRAMS DIVISION (STR ERRATA) 

WASHINGTON 25, D. C. 

A master errata sheet will be compiled from these reports and sent 
to recipients of the volume. Your help will make this book more 
useful to other readers and will be of great value in preparing any 
revisions. 


i fl 


it HI c 

i 


SUlMM4RYjjr|j:igJICAL REPORT OF DIVISION 6, NDRC 


Ubr3!ifSast!cr‘-"“^ 


METHODS OF 


SUBMARINE BUOYANCY 

CONxkoL 

dettassified 

By authority Secretary of 

OCT iyi960 

Defense memo 2 August 1960 

OFFICE OF SCIENTIFIC RESEARCH Alj ^eRaS YEdtE) 

VANNEVAR BUSH, D ^lECTOR 

NATIONAL DEFENSE RESEARCH COMMITTEE 
JAMES B. CONANT, CHAIRMAN 


DIVISION 6 
JOHN T. TATE, CHIEF 


“Sent, all 

MUST 


WASHINGTON, D. C., 1946 


li Jt.S I ITf. 


declasM^SON^ 
oc , 1 3 >96U 


James B. Conant, Chairman 
Richard C. Tolman, Vice Chairman 
^^0^ Adams Army Representative! 


Defense memo 2 ^'^^'^^Prank B. Jewett Navy Representative^ 

Compton Commissioner of Patents^ 

^ Irfen Stewart, Executive Secretary 


^Army representatives in order of service: 


Maj. Gen. G. V. Strong 
Maj. Gen. R. C. Moore 
Maj. Gen. C. C. Williams 
Brig. Gen. W. A. Wood, Jr. 


Col. L. A. Denson 
Col. P. R. Faymonville 
Brig. Gen. E. A. Regnier 
Col. M. M. Irvine 




-Navy representatives in order of service: 

Rear Adm. H. G. Bowen Rear Adm. J. A. Purer 

Capt. Lybrand P. Smith Rear Adm. A. H. Van Keuren 

Commodore H. A. Schade 
^Commissioners of Patents in order of service: 
Conway P. Coe Casper W. Ooms 


OR AN- PAST OF TI^ 

document, all CLASSIFICATJION 


ORGANIZATION OF NDRC 


The duties of the National Defense Research Committee 
were (1) to recommend to the Director of OSRD suitable 
projects and research programs on the instrumentalities of 
warfare, together with contract facilities for carrying out 
these projects and programs, and (2) to administer the tech- 
nical and scientific work of the contracts. More specifically, 
NDRC functioned by initiating research projects on re- 
quests from the Army or the Navy, or on requests from an 
allied government transmitted througli the Liaison Office 
of OSRD, or on its own considered initiative as a result of 
the experience of its members. Proposals prepared by the 
Division, Panel, or Committee for research contracts for 
performance of the work involved in such projects were 
first reviewed by NDRC, and if approved, recommended to 
the Director of OSRD. Upon approval of a proposal by the 
Director, a contract permitting maximum flexibility of 
scientific effort was arranged. The business aspects of the 
contract, including such matters as materials, clearances, 
vouchers, patents, priorities, legal matters, and administra- 
tion of patent matters were handled by the Executive Sec- 
retary of OSRD. 

Originally NDRC administered its work through five 
divisions, each headed by one of the NDRC members. 
These were: 

Division A — Armor and Ordnance 
Division B — Bombs, Fuels, Gases, 8c Chemical Problems 
Division C — Communication and Transportation 
Division D — Detection, Controls, and Instruments 
Division E — Patents and Inventions 


IV 


In a reorganization in the fall of 1942, twenty-three ad- 
ministrative divisions, panels, or committees were created, 
each with a chief selected on the basis of his outstanding 
work in the particular field. The NDRC members then be- 
came a reviewing and advisory group to the Director of 
OSRD. The final organization was as follows: 

Division 1 — Ballistic Research 

Division 2 — Effects of Impact and Explosion 

Division 3 — Rocket Ordnance 

Division 4 — Ordnance Accessories 

Division 5 — New Missiles 

Division 6 — Sub-Surface Warfare 

Division 7 — Fire Control 

Division 8 — Explosives 

Division 9 — Chemistry 

Division 10 — Absorbents and Aerosols 

Division 1 1 — Chemical Engineering 

Division 12 — Transportation 

Division 13 — Electrical Communication 

Division 14 — Radar 

Division 15 — Radio Coordination 

Division 16 — Optics and Camouflage 

Division 17 — Physics 

Division 18 — War Metallurgy 

Division 19 — Miscellaneous 

.\pplied Mathematics Panel 

Applied Psychology Panel 

Committee on Propagation 

Tropical Deterioration Administrative Committee 

1 arv of Congress 




2015 


490951 


DECLASSIFIED 

NDRC FOREWORI^y authority Secretary of 


A S EVENTS of the years preceding 1940 revealed more 
^and more clearly the seriousness of the world situ- 
ation, many scientists in this country came to realize 
the need of organizing scientific research for service 
in a national emergency. Recommendations which 
they made to the White House were given careful and 
sympathetic attention, and as a result the National 
Defense Research Committee [NDRC] was formed 
by Executive Order of the President in the summer of 
1940. The members of NDRC, appointed by the 
President, were instructed to supplement the work of 
the Army and the Navy in the development of the 
instrumentalities of war. A year later, upon the estab- 
lishment of the Office of Scientific Research and De- 
velopment [OSRD], NDRC became one of its units. 

The Summary Technical Report of NDRC is a 
conscientious effort on the part of NDRC to sum- 
marize and evaluate its work and to present it in a 
useful and permanent form. It comprises some sev- 
enty volumes broken into groups corresponding to 
the NDRC Divisions, Panels, and Committees. 

The Summary Technical Report of each Division, 
Panel, or Committee is an integral survey of the work 
of that group. The first volume of each group’s report 
contains a summary of the report, stating the prob- 
lems presented and the philosophy of attacking them 
and summarizing the results of the research, devel- 
opment, and training activities undertaken. Some 
volumes may be “state of the art” treatises covering 
subjects to which various research groups have con- 
tributed information. Others may contain descrip- 
tions of devices developed in the laboratories. A 
master index of all these divisional, panel, and com- 
mittee reports which together constitute the Sum- 
mary Technical Report of NDRC is contained in a 
separate volume, which also includes the index of a 
microfilm record of pertinent technical laboratory 
reports and reference material. 

Some of the NDRC-sponsored researches which 
had been declassified by the end of 1945 were of suffi- 
cient popular interest that it was found desirable to 
report them in the form of monographs, such as the 
series on radar by Division 14 and the monograph on 
sampling inspection by the Applied Mathematics 
Panel. Since the material treated in them is not dupli- 
cated in the Summary Technical Report of NDRC, 




the monographs are an ifnportant part of the story of 
these aspects of NDRC research. 

In contrasf^^ffi^¥nW>9ffl2tfe^oi?fSSar,^wftich is of 
widespread ^fo^teftBS^leased to 

the public, the research on subsurface warfare^ is 
largely Classified and is of general interest to a mofe 
restrict^l group. As a consequence, the report wf 
Division 6 is found almost entirely in its Summary 
Technical Report, which runs to over twenty vol- 
umes. The extent of the work of a Division cannot 
therefore be judged solely by the number of volumes 
devoted to it in the Summary Technical Report of 
NDRC: account must be taken of the monographs 
and available reports published elsewhere. 

Any great cooperative endeavor must stand or fall 
with the will and integrity of the men engaged in it. 
This fact held true for NDRC from its inception, and 
for Division 6 under the leadership of Dr. John T. 
Tate. To Dr. Tate arid the men who worked with 
him— some as members of Division 6, some as repre- 
sentatives of the Division’s contractors— belongs the 
sincere gratitude of the Nation for a difficult and 
often dangerous job well done. Their efforts contrib- 
uted significantly to the outcome of our naval opera- 
tions during the war and richly deserved the warm 
response they received from the Navy. In addition, 
their contributions to the knowledge of the ocean 
and to the art of oceanographic research will assur- 
edly speed peacetime investigations in this field and 

;iNG 

Chief 
ily pre- 
^^Idcly Varied re- 
fevelopment programs but is essentially a 
record of the unstinted loyal cooperation of able men 
linked in a common effort to contribute to the de- 
fense of their Nation. To them all we extend our 
deep appreciation. 



Vannevar Bush, Director 
Office of Scientific Research and DevelopTnent 


J. B. CoNANT, Chairman 
National Defense Research Committee 




FOREWORD 


I MPROVEMENT o£ performance in many operations 
carried out by Service personnel may be brought 
about through an understanding of the physical fac- 
tors involved and by a scientific analysis of the opera- 
tion. How true this is in the important operation of 
diving a submarine is illustrated in this report. 

This report summarizes an applied research proj- 
ect conducted by the staff of the Woods Hole Oceano- 
graphic Institution in such close cooperation with 
the Navy that it may most accurately be described as 
a joint Navy-NDRC project. The Division is deeply 
appreciative of the facilities for experimentation pro- 
vided by the Navy and for the opportunities given for 
the observation of operations which were made freely 


available to the staff of the Institution. In particular, 
the Division is greatly indebted to Dr. A. C. Redfield 
of the Woods Hole staff, who undertook the prepara- 
tion of this report. 

Undoubtedly, as the design of submarines is modi- 
fied and as further studies of oceanographic condi- 
tions provide additional data, the operating practices 
will require modification. This report, however, em- 
phasizes factors of general applicability and discusses 
methods which may be employed in an even more 
refined analysis of the operations here discussed. 

John T. Tate 
C hief, Division 6 





PREFACE 


T he primary aim of this volume is to clarify the 
problems encountered in diving a submarine. In 
the early days of submarine operation, the ballast ad- 
justments were made mainly by feel and by accumu- 
lated experience. Gradually diving officers came to 
realize that relatively large changes in the density of 
the water with depth would sometimes be encoun- 
tered. Lacking contact with oceanography, however, 
they did not suppose that such conditions were pre- 
dictable or could in any way be charted. The possi- 
bility of encountering unexpectedly marked density 
changes made it advisable to be somewhat cautious in 
diving through a considerable depth range. 

Once it was realized that the distribution of tem- 
perature and salinity in the sea directly affected sub- 


marine diving operations, measurements of the effects 
and the charting of the available oceanographic data 
in a form convenient to the diving officer were under- 
taken. During the war period most of the studies of 
the performance of submerged submarines and of the 
compressibility of their hulls had to be carried out 
during the course of training activities. The precision 
and completeness of the data presented in this vol- 
ume, therefore, leave much to be desired. Diving 
officers have found, however, that even rough meas- 
urements and a general understanding of the factors 
influencing the distribution of density in the sea can 
be helpful. 

A. C. Redfield 



ix 





CONTENTS 


1 Introduction 

2 . Density Gradients in the Sea 

3 Theory of Trim Adjustment in Diving .... 

4 Practical Units and Relations 

5 Compression 

6 The Prediction of Buoyancy Changes Due to Density 

Gradients in the Sea 

7 Changes in Buoyancy During Prolonged Submergence 

8 Stable Buoyancy 

9 The Use of Planing Forces to Control Depth . 

10 The Uses of the Submarine Bathythermograph 

in Operations 

1 1 Submarine Supplements to the Sailing Directions 

12 The Problem of Resubmergence 

Glossary 

Bibliography 

Contract Numbers 

Service Project Numbers 

Index 


PAGE 

1 

3 

12 

14 

17 

25 

39 

46 

51 

55 

59 

72 

75 

77 

79 

80 

81 




Chapter 1 

INTRODUCTION 


W HEN A SUBMARINE is at the surface, its weight is 
supported in part by the displacement of the 
main ballast tanks which are filled with air. When it 
submerges, these tanks are filled with water and no 
longer have a buoyant effect. It is then essential that 
the weight of the vessel be very nearly equal to that of 
the water which it displaces. Only under this condi- 
tion can its depth be controlled by adjustments of the 
angles of the diving planes and of the hull. 

Fine adjustments in weight are made by changing 
the quantity of water in the auxiliary or other vari- 
able ballast tanks, and when this is satisfactorily ac- 
complished the submarine is said to be in trim. 

The basic condition for submarine operation is a 
state of trim at periscope depth. From there it may 
return to the surface merely by refilling the main bal- 
last tanks with air. This is an “all or none” operation 
requiring no careful adjustment since relatively large 
variations in buoyancy are tolerable in the surfaced 
vessel. So long as it remains submerged, however, 
trim must be adjusted to the end that the buoyancy 
forces may be kept within the control of the dynamic 
forces arising from the diving planes as the vessel 
moves through the water. 

If the submarine changes its depth substantially, 
an adjustment in trim is required for several reasons. 
As the depth increases, the pressure due to the over- 
lying water compresses the hull, and since its displace- 
ment is decreased, it becomes less buoyant. The in- 
crease in pressure with depth also compresses the sea 
water and thus increases its density. This serves to in- 
crease the buoyancy of the submarine. With subma- 
rines of present construction the compression of the 
hull exceeds the compression of sea water and the 
resultant effect of increasing depth is a decrease in 
buoyancy. 

Since the compression of sea water and the com- 
pression of the hull are proportional to the depth, for 
any particular submarine the adjustment in ballast 
required to compensate for the change in buoyancy 
with depth can be allowed for simply, if other condi- 
tions affecting buoyancy are constant. Many diving 
officers have developed rules, based on their experi- 
ences, for the amount of ballast to be pumped out on 
descent. In practice, however, great uncertainty ac- 


companies the use of such rules because the density of 
the sea water in which the submarine may operate 
frequently varies with depth. 

If the temperature and salinity of sea water were 
uniform throughout the depth of submergence, these 
simple rules based on the compression effects would 
be adequate for trim adjustment. However, when the 
temperature and salinity of the water change with 
depth so as to increase substantially the density of the 
deeper layers, the weight of the water displaced by a 
descending submarine increases and the vessel be- 
comes more buoyant. If the effects of compression 
were negligible, water would need to be flooded into 
the auxiliary tanks until the weight of the vessel 
equaled the increased weight of the water it displaced. 

When the effects of compression and the presence 
of a density gradient due to temperature or salinity 
changes are simultaneously considered, the presence 
of the density gradient will always decrease the 
amount of ballast water which must be pumped out 
on account of compression. If the density gradient is 
sufficiently strong, it will overbalance the effect of 
compression, and water must be flooded in on descent 
instead of being pumped out as required by the 
compression. 

Submariners have long been aware that such den- 
sity gradients exist, for when strongly developed they 
may retard the descent or ascent of the submarine. 
Strong gradients of this sort are known in the Service 
as density layers. Frequently, density layers are en- 
countered strong enough to permit the submarine to 
float supported by the denser medium, or balance, 
without using the planes to control depth. Formerly, 
this maneuver was discouraged because of the uncer- 
tainty of the operation when the hydrography of the 
water is unknown. 

Prior to 1943 submarines were not equipped with 
instruments to inform the diving officer whether den- 
sity gradients existed in the water into which he sub- 
merged. Adjustments in trim were made entirely by 
trial. Under these conditions much time is frequently 
consumed in pumping and flooding ballast before 
satisfactory control is obtained. In peacetime exer- 
cises, when submarines may be controlled at high 
speed by the use of the diving planes, regardless of 


1 


2 


INTRODUCTION 


exact adjustments of buoyancy, these difficulties were 
relatively unimportant. 

In wartime, the necessity for maneuvering rapidly 
and silently becomes compelling. When submarines 
are sent into unfamiliar waters and may need to sub- 
merge in the greatest haste, delay in reaching the de- 
sired depth results, and the period of noisy operation 
of the ballast pumps is prolonged. The uncertainty 
of the operation must add greatly to the mental strain 
of the men concerned. The magnitude of the uncer- 
tainty is reflected in the report of a submarine which, 
early in the war, was on patrol in Japanese waters: 

“Off Fuji Wan we encountered the heaviest density layer 
for the cruise. At 160-foot depth it was necessary to flood 
7,000 pounds to auxiliary instead of removing 7,000 pounds 
as is customary— a total of 14,000 pounds difference.” 

Since it may take as much as one minute to pump 
1,000 pounds of ballast water out of the tanks, the 
delays on encountering such a condition unex- 
pectedly may be very great. 

From the foregoing, it is apparent that to bring his 
vessel into good trim at a desired depth with the 
greatest speed and precision, the diving officer should 
know in advance the way in which the buoyancy of 
the water (density) will vary with depth. This infor- 
mation might be obtained from a suitable instrument 
lowered from the vessel, but it is more practical to 
have the instrument carried down by the submarine, 
since this not only permits information for subse- 


quent use to be secured by an exploratory dive, but 
also indicates the conditions which are being en- 
countered while a dive is under way. 

The submarine bathythermograph [BT]^ is an in- 
strument which draws a graphic record of the tem- 
perature of the sea water as a function of depth as the 
submarine descends. The instrument was designed as 
an aid in predicting sound ranges, but found almost 
immediate application as an aid to the diving officer, 
since the density gradients encountered in diving are 
due very largely to changes in temperature with 
depth. A more elaborate instrument, the Model 
CXJC, which measures the temperature and salinity 
of the sea water and computes their effect on the 
buoyancy of the submarine is now being perfected. 

The following chapter presents an account of the 
various kinds of density gradients which occur in the 
sea and a discussion of the conditions which bring 
them about and the situations in which they are apt 
to be encountered. The remainder of the volume is 
devoted to a discussion of the factors which influence 
the buoyancy of submarines during submergence and 
the use of bathythermographs in controlling diving 
operations. 

a The abbreviation BT is used because of its widespread 
adoption by Navy and civilian personnel working with bathy- 
thermographs. The author points out that this usage is unoffi- 
cial and does not have his backing. Bathythermograph is the 
acceptable form but BT appears in this volume when used as an 
adjective. 



Chapter 2 

DENSITY GRADIENTS IN THE SEA 


T he general principles of oceanography and their 
relation to naval problems is reviewed in Volume 
6 A, Division 6 of the Summary Technical Report. 
The conditions which give rise to gradients of tem- 
perature and salinity in various parts of the ocean are 
discussed there in some detail. The relations of tem- 
perature and salinity to density are of particular im- 
portance to submarines since they determine the 
buoyancy conditions encountered in diving. These 
relationships are discussed in greater detail in this 
chapter. 

The true density of sea water, p, is influenced by 
its temperature, its salinity, and the pressure under 
which it exists. The increasing density of sea water 
which results from compression with depth may be 
disregarded in connection with the buoyancy of sub- 
marines since it is taken into account in estimating 
the apparent compression of the submarine’s hull. 
The effective density of the sea water may be esti- 
mated from its temperature and salinity, assuming it 
to be under a pressure of one atmosphere, as at the 
sea’s surface. This function of temperature and salin- 
ity is represented by p^g. The term density will be 
used to refer to this function.*^ 

A change in density of 0.001 changes the buoyancy 
of a fleet-type submarine by approximately 5,400 
pounds. The effect of a change in temperature on the 
density of sea water and on the resulting buoyancy 
of such a submarine varies with the temperature of 
the water, as shown in Figure 1. A change in salinity 
of one part per thousand changes the density by 
0.00078 and alters the buoyancy of such a submarine 
by 4,200 pounds. The effects of salinity and tempera- 
ture are additive. These and other quantitative rela- 
tions are considered in greater detail in Chapter 4. 

The temperature of the sea’s surface and its fresh 
water tributaries range from 28 to 90 F, depending on 
latitude and season. The salinity may lie anywhere 
between 0 and 40 parts per thousand. The changes in 

a The density function is expressed in grams per cubic 
centimeter. In oceanography the specific gravity of sea water is 
defined relative to pure water at 4 C. Consequently the numeri- 
cal values of density and specific gravity are the same and values 
of p^^ may be used to express specific gravity. This is done in the 
practical solution of buoyancy problems as explained in Chap- 
ter 4. 


density which result from such variations in tempera- 
ture and salinity, and their estimated effects on the 
buoyancy of a submerged submarine of 2,400 tons 
displacement are as follows: 



Limits of 
variation 

Resulting 

density 

change 

Resulting 

buoyancy 

change 

Temperature 

28-90 F 

0.0072 

39,000 pounds 

Salinity 

0-40 Voo 

0.0312 

168,000 pounds 

Total 


0.0384 

207,000 pounds 


Since changes of this magnitude are not likely to be 
encountered at any one time or place, the figures are 
of interest only in showing the magnitude of the com- 
pensation which a submarine must be designed to 
make on this account, and in indicating the range of 
conditions to which density recording devices should 
be adapted. 

Except where wind, tide, and other currents lead to 
violent mixing, the temperature and salinity of sea 



Figure 1. Effect of temperature on the density of sea 
water having a salinity of 35 Voo and corresponding effect 
on buoyancy of a submarine of 2,400 tons submerged 
displacement. 


3 


4 


DENSITY GRADIENTS IN THE SEA 


water at any one place is far from uniform. Exchanges 
of heat take place through the sea’s surface and addi- 
tions or losses in water also occur at the surface 
through precipitation and evaporation. Conse- 
quently, temperature and salinity and the resulting 
density frequently change with depth. On the other 
hand, water of a given density tends to seek its own 
level and to spread uniformly for relatively great dis- 
tances in a horizontal direction. Consequently, the 
sea has a stratified structure, composed of horizontal 
layers of different quality lying one upon another. 

The maximum change in temperature and salinity 
which a submarine is likely to encounter in a single 
dive from periscope depth and the related density 
and buoyancy changes are about as follows: 



Maximum 

change 

Resulting 

density 

change 

Resulting 

buoyancy 

change 

Temperature 

30 F 

0.00420 

22,600 pounds 

Salinity 

2.5 Voo 

0.00195 

10,500 pounds 

Total 


0.00615 

33,100 pounds 


These figures bring out the fact that under extreme 
conditions salinity changes are responsible for only 
about one-third of the density change likely to be 
encountered. 

The estimate of the maximum likely buoyancy 
change given above exceeds somewhat the maximum 
figure recorded by American submarines operating 
in the Pacific war area which is about 26,000 pounds. 
1 he frequency with which different amounts of bal- 
last have been actually pumped out or Hooded in, in 
the course of deep dives while in service under recent 
wartime conditions, is indicated by Figure 2. This 
histogram is based on notations on bathythermo- 
graph cards returned by 49 submarines and repre- 
sents the record of 336 dives made in the course of 
training, in transit to patrol areas, and while on 
patrol in the western Pacific Ocean. 

While the ballast pumped on descent rarely ex- 
ceeds 4,000 pounds it is not uncommon to flood 8,000 
to 10,000 pounds and occasionally much larger ad- 
justments are made. In Figure 2 the class in which 
the ballast change was plus or minus 500 pounds was 
composed largely of dives in which there was no 
change of ballast. This class is of exceptional size and 
the two adjacent classes are of relative deficiency 
because small maladjustments of trim are frequently 
disregarded in diving, and no change in ballast is 



THOUSANDS OF POUNDS 


Figure 2. Frequency distribution of ballast changes made 
in deep dives by fleet-type submarines in service. 

ordinarily made unless the net buoyancy becomes 
more than one or two thousand pounds. 

2 1 STABILITY OF THE WATER COLUMN 

Layers of sea water of higher density cannot exist 
long above layers of lower density since, being 
heavier, they sink through the lighter layers and mix 
with them. When conditions arise which increase the 
density of the surface layers of the sea, such as cooling 
in the fall of the year or rapid evaporation, mixing 
processes are set up which tend to bring the surface 
layers to a condition of homogeneous temperature 
and salinity. Negative density gradients cannot exist 
permanently in the sea because the condition is 
unstable. 

On the other hand, if the density of the surface 
waters is less than that of the deeper layers a stable 
condition exists which tends to be permanent. Work 
must be done to cause the lighter layers to mix with 
those beneath and thus the mixing action of wind 
and tide are retarded. When conditions are favorable 
for the formation of stable conditions, such as the 


MIXED WATER 


warming of the surface waters in early summer, the 
condition not only persists, but increases because the 
surface layers are kept from mixing with those be- 
neath and the heat absorbed from the sun and the 
acquisitions of fresh water from rainfall remain con- 
centrated in the upper layers. 

The compression of the water with depth does not 
influence the stability of the water column. Within 
such depths as are reached by submarines, the con- 
tribution of temperature and salinity to density, pfg, 
alone need to be taken into account in determining 
stability. Stability is defined as the rate of change of 
density with depth or by dpfg/dZ where Z is the 
depth. Negative values of stability are highly excep- 
tional and cannot exist except as the result of very 
active processes. 

2 2 MIXED WATER 

Wherever the forces of wind, tide, and current are 
strong enough to overcome the influences which lead 
to stable stratification, the sea water becomes thor- 
oughly mixed. The completeness of the process is in- 
dicated by the uniformity of the temperature, and 
such water is frequently referred to as isothermal. 
The thorough mixing indicated by the uniform tem- 
perature usually may be assumed to produce a uni- 
form distribution of salinity. Consequently, isother- 
mal water is generally devoid of density gradients. 

Shallow isothermal layers exist very generally at 
the immediate sea surface where wave action mixes 


the water. Layers extending deep enough to influ- 
ence submarine operation are more restricted. In the 
tropical and subtropical oceans deep isothermal layers 
of warm water occur at the surface which, in the trade 
wind belts, may extend to three or four hundred feet 
in depth. In temperate regions the upper layers of the 
sea are thermally stratified during the summer season, 
but as the solar radiation weakens in the fall the mix- 
ing processes prevail and the mixed layer at the sur- 
face grows in depth until it extends by midwinter to 
300 feet or more below the surface. The seasonal 
change in the depth of the mixed water in the North 
Atlantic in the vicinity of Bermuda is shown in Fig- 
ure 3. 

One situation exists in which density gradients may 
occur in water which is practically isothermal. In 
the wet tropics the sea surface may obtain additions 
of fresh water which are of nearly the same tempera- 
ture as the sea water. A salinity gradient consequently 
develops near the surface. Figure 4 illustrates such a 
condition which has been observed off the west coast 
of Africa. Although the water was essentially of uni- 
form temperature to a depth of 150 feet a salinity 
gradient occurred above this depth which increased 
the density by an amount which would alter the buoy- 
ancy of a submarine by 7,500 pounds in the course of 
a dive to the lower limit of the isothermal layer. 
Similar conditions have been observed in the south- 
western Pacific Ocean. 

It is possible that a similar situation may arise 
along the coasts of temperate regions during early 



Figure 3. Distribution of temperature in the upper layers of the North Atlantic Ocean, in neighborhood of Bermuda 
throughout the year. 


6 


DENSITY GRADIENTS IN THE SEA 



DENSITY CHANGE 


0 .001 .002 .003 .004 .005 



Figure 4. Distribution of temperature, salinity, and density in the upper layers of the Atlantic Ocean at 5° 36' N, 
23° 25' W. Apf. shows effect of the temperature gradient, Ap^ the effect of the salinity gradient, and Ap^g their com- 
bined effect on density. The corresponding effect on the buoyancy of a submerged submarine of 2,400 tons displace- 
ment is shown, in thousands of pounds, on the scale marked Buoyancy Change. 


spring wherever melting snows bring large quantities 
of fresh water at nearly freezing temperature into the 
sea when its temperature also is near freezing point. 
However, such situations would be very local and 
temporary and the density gradients produced would 
probably be too near the surface to affect diving 
operations. 

Except in these rather limited situations, compres- 
sion with depth alone need be considered when a 
submarine dives in isothermal water. 


23 NEGATIVE TEMPERATURE 

GRADIENTS 

Sea water is usually warmer at the surface than at 
some greater depth. The layer of water in which tem- 
perature decreases sharply with depth is called the 
thermoclme. The strong density layers encountered 
by submarines are commonly due to the negative tem- 
perature gradients encountered in passing through a 
thermocline. 



Figure 5. Distribution of temperature in the upper layers of the Gulf of Maine throughout the year. 


NEGATIVE TEMPERATURE GRADIENTS 


7 


DEGREES FAHRENHEIT 



Figure 6. Exceptionally strong negative temperature 
gradient recorded by bathythermograph of a U. S. sub- 
marine in the Yellow Sea in September. 

Negative temperature gradients arise in two ways; 
first, the warming of the surface by the sun, and sec- 
ond, the flow of warm water layers over colder masses 
of water as the result of currents. 

In temperate latitudes, where the sea is uniformly 
chilled in the winter, strong temperature gradients of 
the first type develop each summer. Their develop- 
ment runs a characteristic course illustrated in Figure 
5, the gradients becoming stronger as the season ad- 
vances and never extending very deep. With the cool- 
ing of the surface water in the fall the gradient is 
rather abruptly destroyed and becomes deeper as this 
takes place. 

Shallow gradients are particularly well developed 
along the eastern coasts of Asia and North America. 
The density layers which they produce along the 
New England coast in summer are familiar to Ameri- 
can submariners. Figure 6 illustrates an exceptionally 
strong gradient of this sort recorded by a submarine 
operating in the Yellow Sea in September. It was 
necessary to flood 20,000 pounds of ballast to pene- 
trate below this layer. 

The second general type of temperature gradient 
arises from the circumstance that the basins of the 
ocean are everywhere filled with cold water. This is 
water which has been chilled and sunk in high lati- 
tudes. In tropical and subtropical regions the surface 
water is warmed, frequently to about the temperature 
of the air. The warm layer is always relatively thick, 
is usually thoroughly mixed, and often extends to 
greater depths than are reached in submarine opera- 
tions. The temperature gradients marking the transi- 



Figure 7. A deep-lying negative temperature gradient 
recorded by bathythermograph of a U. S. submarine in 
the Japan Current. 

tion are much less abrupt than those found in the 
shallow summer thermoclines and usually extend 
downward for several hundred feet, to beyond the 
limits reached in diving. The thickness of the warm 
surface layer depends very much on the local char- 
acter of the ocean currents. In areas toward which the 
surface waters move (convergences) the warm layer 
becomes very thick. In areas away from which the 
surface water is carried by its motion the temperature 
gradient approaches much closer to the surface. 

It may be seen that the two types of temperature 
gradient which have been described depend on the 
nature of the climate in which they are established. 
Wherever cold water is becoming warmer, either be- 
cause of a change in season or because of the flow of 
water to warmer regions a shallow gradient, often of 
great strength, results. The increasing stability of the 
water as it warms does not permit the water to warm 
to great depths. Cold currents consequently are char- 
acterized by strong shallow temperature gradients. 
Wherever the climate is warm throughout the year 
the surface water is heated to considerable depths. If 
such water is carried to cooler regions in the course of 
its circulation, heat is lost from the surface. Cooling 
the surface creates an unstable condition which leads 
to thorough mixing. The layer of mixed water above 
the temperature gradient remains thick or is thick- 
ened in the process. Warm currents consequently are 
characterized by deep-lying temperature gradients. 
An example recorded from the Kuroshio Current off 
Japan is illustrated in Figure 7. 

It should be unnecessary to point out that in many 




8 


DENSITY GRADIENTS IN THE SEA 


regions much more complicated temperature pat- 
terns are found. These arise from the mixing of di- 
verse waters particularly at the junction of currents. 
However, the two types of temperature gradient de- 
scribed are characteristic of large portions of the sea 
and the more complicated patterns are usually to be 
derived from them. 

24 SALINITY GRADIENTS 

Salinity gradients arise from (1) the dilution of the 
surface by rainfall, melting ice, and the run-off from 
the land, (2) evaporation of water from the sea’s sur- 
face, and (3) the flow of waters of different salinity 
over one another as the result of ocean currents. 

In temperate regions there is usually an excess of 
rainfall over evaporation and consequently positive 
salinity gradients tend to develop beneath the sea’s 
surface. Along the coasts of such regions the outflow 
from rivers very greatly augments this effect and sub- 
stantial density gradients result from the dilution of 
the upper layers of water. It follows that the shallow 
temperature gradients characteristic of temperate re- 
gions in summer are accompanied by salinity gradi- 
ents. These gradients are particularly strong in 
coastal regions. Both kinds of gradient cause the 


water to be more dense as depth increases, that is, they 
supplement one another in developing the stability 
of the water column. 

It may be observed from Figure 8, which shows the 
gradient of temperature, salinity, and resulting den- 
sity in a situation of this sort, that the gradients of 
temperature and salinity very closely coincide in 
depth. This arises because the surface waters are pre- 
vented from mixing with the deeper waters by the 
sharp density gradient while both above and below 
the water mixes more freely. Both gradients conse- 
quently tend to develop in the same relation to the 
resulting density pattern. During the winter when 
the disappearance of the temperature gradient de- 
creases the stability of the water, the mixing which 
results destroys the salinity gradient also. In spring 
the melting of snows and the rainfall characteristic 
of the season leads to the early development of the 
salinity gradient. This becomes relatively less impor- 
tant than the temperature gradient in determining 
the density distribution as the summer season ad- 
vances. 

In warm oceanic areas salinity gradients are less 
pronounced and thus of minor importance in deter- 
mining the density distribution in the upper layers of 
the sea. In substantial areas of small rainfall in the 


TEMPERATURE — “F 
30 40 50 60 70 



SALINITY— %o 
31 32 33 



DENSITY CHANGE 

0 .001 .002 .003 .004 



Figure 8. Distribution of temperature, salinity, and density in the upper layers of the Gulf of Maine at 42° 55' N, 
70° 15' W in September. Ap^ shows the effect of the temperature gradient, Ap^ the effect of the salinity gradient, 
and Apfg their combined effect on density. The corresponding influence on the buoyancy of a submerged submarine 
of 2,400 tons displacement is shown, in thousands of pounds, on the scale marked Buoyancy Change. 


SALINITY GRADIENTS NEAR RIVER MOUTHS 


9 



Figure 9. Ocean areas where salinity gradients may be expected to influence submarines when diving. 


subtropics evaporation exceeds precipitation and the 
most saline water is found at the surface. Such salinity 
gradients in the surface layers are small and may be 
associated with similarly small positive temperature 
gradients with the result that the density of the water 
column is nearly uniform. In the wet tropics, on the 
other hand, rainfall may very substantially reduce the 
salinity of the surface layers with the result that 
strong gradients of density are produced. The density 
layers familiar to submariners operating in the Gulf 
of Panama are due in part to this. Similar situations 
are encountered off the west coast of Africa and in the 
East Indies. 

In general, it may be said that salinity gradients 
play a minor role in producing density gradients large 
enough to affect submarine operations in the greater 


part of the open oceans. Along the coasts of temperate 
regions in the spring and summer and in the wet 
tropics substantial density gradients result from re- 
duction of the salinity of the surface layers. The areas 
in which salinity changes are known to occur which 
produce gradients in density of as much as 0.001 
within 300 feet of the surface are shown in Figure 9. 
Within these areas ballast adjustment of as much as 
6,000 pounds may be required in diving for this cause 
alone. 

2 5 SALINITY GRADIENTS NEAR RIVER 
MOUTHS 

The fresh water flowing from the mouths of rivers 
tends to flow over the surface of the sea water, some- 
times for very great distances. The strong density 


DENSITY CHANGE 

0 .001 .002 .003 .004 .005 .006 .007 .008 



Figure 10. Effect of temperature and salinity gradients on density in tbe upper layers of tbe Atlantic off tbe Amazon 
River at 3° 10' N, 49“ 29' W. Apf shows tbe effect of tbe temperature gradient, Ap^ tbe effect of tbe salinity grad- 
ient, and Apfg tbeir combined effect. Tbe resulting influence on tbe buoyancy of a su])merged submarine of 2,400 
tons displacement is shown on the lower scale. 




10 


DENSITY GRADIENTS IN THE SEA 


gradients which arise in this way are, however, very 
shallow and usually do not extend deep enough to 
affect submarine operations at or below periscope 
depth as much as might be expected from the reduced 
density of the surface. This fact is illustrated by Fig- 
ure 10, which shows the gradients occasioned by the 
outflow of the Amazon. 

Since currents must flow parallel to coasts, the 
water of reduced salinity which is formed near the 
mouths of rivers tends to spread along the coast in- 
stead of flowing out to sea. Continuous bands of 
water of low salinity are consequently formed along 
coasts in areas of adequate rainfall. 

26 POSITIVE TEMPERATURE 

GRADIENTS 

A positive temperature gradient cannot persist un- 
less accompanied by a positive salinity gradient. This 
is because in the absence of a salinity gradient the 
water column will be unstable if the upper layers are 
colder and thus more dense than those below. The 
salinity gradient must increase the density with depth 
at least as much as the positive temperature gradient 
decreases it if an unstable condition is to be avoided. 

Rather weak positive temperature gradients may 
be produced by the cooling of the surface during the 
fall and winter in temperate regions when salinity 
gradients are present. These effects are not large and 


are too near the surface to concern submarines in 
diving. More extensive positive gradients at greater 
depths may be formed by the flow of layers of colder 
water of relatively low salinity over warmer water of 
higher salinity at greater depth. The locations at 
which this situation occurs are limited but happen to 
be frequented by submarines. 

An example of such a situation is found off the 
coast of southern New England in areas visited by 
American submarines for purposes of test and train- 
ing. Near the margin of the continental shelf the 
coastal water tends to flow out over the deeper 
oceanic water. The coastal water is much less saline 
than oceanic water and a pronounced salinity grad- 
ient is formed at a depth of 150 to 250 feet. During 
the winter the coastal water becomes much colder 
than the deeper layers so that a positive temperature 
gradient is formed. Although this cooling increases 
the density of the upper layer the water column re- 
mains stable since the salinity gradient more than 
compensates for the effect of the temperature grad- 
ient. The situation is illustrated by Figure 11 which 
shows the conditions encountered by a submarine in 
April. The temperature increased 10 F between 150 
and 275 feet, yet the density increased 0.0006 in the 
same depths because of an increase in salinity at the 
greater depths of 1.9 Yoo- The submarine was able 
to float balanced in the density gradient at 210 feet in 
spite of the strong positive temperature gradient. 



BUOYANCY CHANGE 


Figure 11. Distribution of temperature, salinity, and density in the upper layers of the Atlantic Ocean near the west- 
ern margin of the Gulf Stream (40° 14' N, 70° 56' W). Ap^ shows effect of the temperature gradient, Ap^ the effect 
of the salinity gradient, and Apfg their combined effect on density. The corresponding influence on the buoyancy of 
a submerged submarine of 2,400 tons displacement is shown, in thousands of pounds, on the scale marked Buoyancy 
Change. 


INTERNAL WAVES 


11 


2.7 INTERNAL WAVES 

Where gradients of temperature or salinity occur 
in the ocean giving rise to changes in density with 
depth, it has frequently been observed that the layers 
of water are in vertical oscillation. These internal 
waves vary greatly in period and amplitude depend- 
ing on circumstances. The waves most frequently ob- 
served in density gradients within the operating 
depths of submarines have periods of 10 or 15 min- 
utes. Waves of longer period, from 2 to 12 hours, have 
also been recorded, the latter apparently being re- 
lated to the tidal rhythm. The amplitude of the waves 
is variable. The short-period waves may have ampli- 
tudes of 10 to 16 feet; amplitudes as great as 45 to 60 
feet have been recorded for the long-period waves. 

Internal waves introduce uncertainty into sub- 
marine operations in two ways. The passage of a 
wave during deep submergence may cause quite dif- 
ferent ballast adjustments to be required on returning 
to a given depth within the density gradient than 
were anticipated from conditions encountered during 
the preceding descent. Very frequently bathyther- 
mograph records on ascent show a quite different 
trace from that obtained in descent owing to the ver- 
tical displacement of the water layers of different 
temperatures. Figure 12 illustrates a tracing of this 
character. 

A submarine operating in a density layer in which 
internal waves occur will tend to rise and sink with 
the wave. This behavior is illustrated in Figure 13 
which shows the changes in depth of a submarine 
while balanced motionless in a density layer off Ports- 
mouth, New Hampshire. The submarine rose and fell 
with a fairly regular rhythm of period of about 15 
minutes. The change in depth varied from 8 to 14 
feet and the maximum rate of rise or fall was 2 feet 
per minute. The observations lasted for over an hour 
during which time the temperature of water samples 
drawn from the sea did not vary more than 1 F. Since 
the submarine lay in a temperature gradient of 0.5 F 
per foot, it was evident that the entire water mass 
was rising and falling carrying the vessel with it. 



Figure 12. Displacement of the temperature trace attrib- 
uted to the passage of an internal wave during the period 
of deep submergence, recorded by bathythermograph of 
U. S. submarine. 

When internal waves of this sort are present it is 
more difficult to maintain constant depth without 
continual adjustment of diving planes or ballast. 
This is a serious disadvantage if it occurs while depths 
suitable for using the periscope must be maintained. 
During deep submergence when exact depth control 
is less important, the change in depth due to internal 
waves may not be inconvenient and the submarine 
may be allowed to rise and fall with the oscillation of 
the water. 



0 10 20 30 40 50 60 


TIME IN MINUTES 

Figure 13. Changes in keel depth of a submarine bal- 
anced in a density gradient showing vertical oscillation 
due to the passage of internal waves. 


Chapter 3 

THEORY OF TRIM ADJUSTMENT IN DIVING 


31 BUOYANCY 

T he net buoyancy of a submerged vessel is the dif- 
ference between the weight of the water which is 
displaced and the weight of the vessel. Net buoyancy, 
B, may be defined by the equation: 

B = pV- W, (1) 

in which p = density of the water, 

y = volume of water displaced by the ves- 
sel, and 

W = weight of the vessel. 

Net buoyancy is positive when the displaced weight 
of water is greater than the weight of the vessel. In 
this case the vessel tends to rise. Net buoyancy is nega- 
tive when the weight of the displaced water is less 
than the weight of the vessel, and in this case the ves- 
sel tends to sink. If the displaced weight of water 
equals the weight of the vessel net buoyancy is zero, 
and buoyancy is said to be neutral. The vessel tends 
neither to rise nor sink. 

Buoyancy forces are static and define the behavior 
of a motionless vessel. In the case of a moving sub- 
marine vertical forces arise from the hull form, its 
fore and aft inclination, and the “lift” of the diving 
planes. These forces increase with speed and make it 
possible to control the depth in the presence of con- 
siderable positive or negative buoyancy. The word 
buoyancy is frequently applied to the buoyant force” 
due to the displaced water. 


a The buoyant force is referred to as pF in the present treat- 
ment. Since it is convenient to break this term down into 
several components in the discussion of submarine problems, 
this restricted use of the word is abandoned and buoyancy is 
used in place of net buoyancy whenever no ambiguity is in- 
volved. The term pV will be referred to as the weight displace- 
ment. 

In the present chapter, net buoyancy and weight are assumed 
to be measured in grams and volume in cubic centimeters. This 
avoids the necessity for introducing dimensional constants into 
the fundamental equations. Conversion to the practical units 
employed in naval architecture and marine engineering are dis- 
cussed in Chapter 4. 


3 2 EFFECT OF CHANGE IN DEPTH 

If the submarine dives to a different depth the 
change in depth is attended with the following 
changes: 

AB = change in net buoyancy, 

AV = change in volume displacement due to 
compression of the hull with depth, 

Ap = change in density of the sea water, 

AW = change in weight due to ballast adjust- 
ments or any other cause. 

The relation of these changes for any change in 
depth, Z, may be derived from equation (1) and are as 
follows: 

AB = pAV-h VAp -AW. (2) 

Ap is the sum of two quantities, Ap^ and Apts which 
may be defined as follows: 

Aps = change in density of sea water due to 
compression with depth. 

^Pts = change in density of sea water due to 
changes in temperature and salinity. 

VAp may consequently be written VApg + V Apts 
and equation (2) becomes: 

AB == pAV + VAp, + VApts - A IF. (3) 

The first two terms of this equation represent re- 
spectively the effect on the net buoyancy of compres- 
sion of the hull and of sea water with depth. The 
change in volume of the hull may be assumed to be a 
linear function of depth. The change in density of sea 
water is known to be essentially a linear function of 
depth which amounts to 1.42x10-® gm per cu cm per 
foot. 

The total effect of compression on net buoyancy is 


12 


TRIM 


13 


consequently a linear function of depth and may be 
expressed by the term CaZ in which C is the coeffi- 
cient of compression, i.e., of buoyancy change per 
unit increase in depth. Hence, CaZ = pAV V Apz- 
Substituting in equation (3) 

AB = VApts + CAZ - AW. (4) 

This is the fundamental equation for estimating 
buoyancy changes in diving. 

33 TRIM 

Submariners employ the term trim to designate the 
adjustment of buoyancy as required by the conditions 
of operation.^ Good trim at any stated speed may be 
defined as the condition where the vessel may be held 
at the desired depth with minimal adjustment of the 
angle of hull and diving planes. The positive or nega- 
tive buoyancy which is consistent with good trim 
decreases rapidly as speed is reduced and at 2 knots 
is about 500 pounds. Stop trim is the condition ob- 
tained when buoyancy is neutral and the submarine 
holds its depth in the absence of the planing forces 
dependent on motion. 

In the case of a submarine in stop trim AB = 0 and 
equation (4) becomes 

AW = VApfs-h CAZ. (5) 

This is the fundamental equation for estimating bal- 
last adjustments in diving. 

In applying equation (5) it should be remembered 
that each term represents an effect on net buoyancy. 
The coefficient of compression C is always negative 
since the loss in buoyancy due to compression of the 
hull of existing submarines is always greater than the 
gain in buoyancy due to compression of sea water. 
Consequently CaZ is a negative quantity on descent 
and a positive quantity on ascent; Aptg niay equal 
zero or may increase with increasing depth. For hy- 
drostatic reasons it never decreases with depth. Since 
buoyancy increases in proportion to V, VApts is a 
positive number on descent and a negative number 
on ascent, except when it equals zero. 

b As employed here, trim refers specifically to what is more 
exactly stated as overall trim and depends upon the total 
weight of the submarine. Trim is also used to designate the dis- 
tribution of weight relative to the center of buoyancy, e.g., to 
the fore and aft trim. 


The term A IT is the change in weight required to 
re-establish trim, that is, to nullify the buoyancy 
changes due to the other terms. Consequently, when 
buoyancy increases W must also increase. That is, 
positive values of AIT indicate ballast to be flooded 
in; negative values of A IT indicate ballast to be 
pumped out. 

The following rules may be deduced from equa- 
tion (5) for predicting the nature of ballast adjust- 
ments. 

1. When Apts = 0 

AW = CAZ. 

Remembering that C is a negative number, ballast 
must be pumped out on descent or flooded in on 
ascent in proportion to the change in depth, if den- 
sity gradients are not present. 

2. When VApts> - CaZ 

AIT is positive on descent; negative on 
ascent. 

If the density gradient has a larger effect on buoyancy 
than the compression effect ballast must be flooded 
in on descent and pumped out on ascent. 

3. When V Apts< — CaZ 

Air is negative on descent; positive on 
ascent. 

If the density gradient has a smaller effect on buoy- 
ancy than the compression effect ballast must be 
pumped out on descent and flooded in on ascent. 

4. When V Apts — — CAZ 

AIT 0. 

If the density gradient has an effect on buoyancy 
equal to the effect of compression with depth no bal- 
last change is required in changing depth. This case 
is known as the isoballast condition. 

The quantitative solution of problems in ballast 
adjustment requires the numerical evaluation of (1) 
the coefficient of compression characteristic of the 
vessel in question, and (2) observations on the density 
of the water in which it is diving. 


Chapter 4 

PRACTICAL UNITS AND RELATIONS 


4 1 THE BALLAST CHANGE 

T he ballast change, ATT, is expressed as the 
weight of water in pounds in conformity to sub- 
marine practice. Ballast flooded is -j- ATE; ballast 
pumped is — ate. 

4 2 the displacement 

In naval architecture displacement is customarily 
expressed as the weight of water displaced by the ves- 
sel. In practical considerations of buoyancy it is con- 
sequently convenient to redefine V as the weight dis- 
placement of the vessel, instead of as the volume dis- 
placement as was done in the preceding chapter. If at 
the same time p is redefined as the specific gravity of 
the sea water, instead of the density, the term Vp will 
retain its original dimensions and the equations pre- 
viously developed may be applied. 

In oceanography the term density is commonly 
applied to the specific gravity of sea water relative to 
that of distilled water at 4 C. According to this con- 
vention specific gravities (relative densities) and true 
density (in grams per cubic centimeter) are numer- 
ically equal, and the same values of p may be used 
to represent either without numerical inconsistency. 
The values of specific gravity according to this usage 
are about 0.001 lower than those commonly employed 
in naval architecture which are referred to the den- 
sity of pure water at 60 F. Thus, weight displacement 
is commonly estimated assuming the specific gravity 
of sea water to be 1.025, which corresponds to a spe- 
cific gravity, or density, of 1.024 according to oceano- 
graphic usage. 

It is often convenient when tabulating data to use 
a special notation in which density, p, is expressed 
by the symbol a which is defined in the following 
manner: 

a = (p - 1) 1,000. 

Thus, if p == 1.0258, a = 25.8. The markings of hy- 
drometer scales are frequently abbreviated similarly. 

The symbol cr^ is used to designate the <t value of 
a sample of sea water of some given temperature and 
salinity when measured at atmospheric pressure. The 


(Tf values correspond to pts as used in equation (5) of 
Chapter 3. These values do not take account of the 
effect of pressure at depth on the density of sea water 
in situ. 

The weight displacement is commonly stated in 
tons, for which purpose the long ton of 2,240 pounds 
is employed. In considering submarine buoyancy 
problems it is more convenient to express displace- 
ment in pounds, since ballast changes are measured 
in this unit. 

For a modern fleet-type submarine the weight dis- 
placement submerged is 2,400 tons or V = 5.4 x 10^’ 
pounds. 

4 3 the effect of density 

ON BUOYANCY 

The effect of density on buoyancy, V Apts, is given 
for a fleet-type submarine by: 5.4 x 10® x change in 
density. It must be assumed that the layers of sea 
water in which the displacement lies are uniform and 
similar to the sample measured. Since this may not be 
the case, samples should be drawn from near the level 
of the center of buoyancy to secure the best repre- 
sentative value. 

4 4 RELATION OF SALINITY 

TO DENSITY 

Salinity is expressed as grams of salt per 1,000 grams 
of sea water. The density of sea water is increased by 
0.00078 when the salinity increases IV 00- An in- 
crease of salinity of IVoo requires the flooding of 
.00078 X 5.4 X 10® = 4,200 pounds of ballast. This re- 
lation is sufficiently correct at temperatures between 
30 and 90 F. 

4 5 RELATION OF TEMPERATURE 
TO DENSITY 

The density of sea water decreases as the tempera- 
ture increases. The curve describing this relation for 
water of S = 35 Voo is shown in Figure 1 of Chapter 
2. Within the range of salinity commonly encoun- 
tered in the open sea, that is, 30 to 35®/oo> the change 




14 


RELATION OF COMPRESSION OF SEA WATER TO DENSITY 


15 


in density produced by any change in temperature 
does not vary greatly with salinity. Consequently, the 
curve in Figure 1 can be used to describe with suffi- 
cient accuracy the relative buoyancy of a 2,400-ton 
submarine when submerged in water of different tem- 
perature but of any constant salinity above SOYoo- 
The following figures show the approximate effect 
of an increase in temperature of 1 degree on the den- 
sity of sea water and on the buoyancy of a submarine 
of 2,400-ton submerged displacement in sea water of 
35Yoo salinity at characteristic temperatures. 


Temperature 

F 

Density 
change 
per 1 F 

Buoyancy 
change 
in lb 
per 1 F 

40 

-0.000060 

-320 

60 

-0.000124 

-670 

80 

-0.000175 

-940 


For fresh water the corresponding figures are: 


Temperature 

F 

Density 

Change 
per 1 F 

Buoyancy 
Change 
in lb 
per 1 F 

40 

0 

0 

60 

-0.000085 

-460 

80 

-0.000151 

-690 


Complete data on the relation of temperature and 
salinity to density are given in Table 1. 

4 6 RELATION OF COMPRESSION OF 
SEA WATER TO DENSITY 

The density of sea water is increased by compres- 
sion by approximately 14.2 x 10~'^ per foot of depth at 
60 F. The value varies slightly with temperature. 


Table 1. Density of Sea Water as a Function of Temperature and Salinity. 
Temperature F 


Salinity 
”/ 00 

30 

35 

40 

45 

50 

55 

60 

65 

70 

75 

80 

85 

90 

0 

-0.22 

-0.05 

0.00 

-0.08 

-0.27 

-0.57 

-0.96 

-1.42 

-2.00 

-2.65 

-3.37 

-4.16 

-5.01 

2 

1.45 

1.61 

1.63 

1.54 

1.33 

1.02 

0.62 

0.13 

-0.45 

-1.10 

-1.84 

-2.64 

-3.49 

4 

3.08 

3.21 

3.22 

3.11 

2.89 

2.56 

2.15 

1.65 

1.06 

0.40 

-0.34 

-1.15 

-2.02 

6 

4.71 

4.81 

4.80 

4.68 

4.45 

4.11 

3.68 

3.18 

2.58 

1.91 

1.16 

0.34 

-0.53 

8 

6.34 

6.44 

6.41 

6.26 

6.00 

5.66 

5.22 

4.70 

4.09 

3.41 

2.66 

1.83 

0.95 

10 

7.95 

8.03 

7.98 

7.82 

7.57 

7.19 

6.74 

6.21 

5.60 

4.91 

4.15 

3.32 

2.43 

12 

9.58 

9.63 

9.57 

9.39 

9.10 

8.74 

8.27 

7.73 

7.10 

6.40 

5.64 

4.79 

3.90 

14 

11.20 

11.23 

11.16 

10.96 

10.67 

10.28 

9.81 

9.25 

8.62 

7.91 

7.15 

6.29 

5.38 

16 

12.83 

12.84 

12.74 

12.53 

12.21 

11.82 

11.33 

10.77 

10.13 

9.42 

8.63 

7.78 

6.86 

18 

14.43 

14.43 

14.32 

14.09 

13.76 

13.35 

12.85 

12.29 

11.63 

10.90 

10.12 

9.26 

8.34 

20 

16.07 

16.05 

15.90 

15.67 

15.33 

14.90 

14.39 

13.81 

13.15 

12.42 

11.62 

10.75 

9.82 

22 

17.67 

17.63 

17.47 

17.21 

16.87 

16.43 

15.91 

15.31 

14.65 

13.90 

13.09 

12.22 

11.29 

24 

19.29 

19.23 

19.06 

18.79 

18.42 

17.98 

17.44 

16.84 

16.17 

15.41 

14.59 

13.71 

12.79 

26 

20.90 

20.82 

20.63 

20.36 

19.98 

19.51 

18.97 

18.36 

17.67 

16.91 

16.08 

15.20 

14.27 

28 

22.51 

22.42 

22.21 

21.91 

21.52 

21.04 

20.49 

19.87 

19.17 

18.41 

17.58 

16.69 

15.74 

30 

24.15 

24.03 

23.80 

23.50 

23.09 

22.60 

22.04 

21.41 

20.70 

19.92 

19.09 

18.20 

17.24 

32 

25.75 

25.62 

25.38 

25.08 

24.64 

24.13 

23.56 

22.92 

22.21 

21.43 

20.59 

19.69 

18.73 

34 

27.36 

27.22 

26.97 

26.63 

26.20 

25.68 

25.10 

24.45 

23.73 

22.94 

22.09 

21.18 

20.22 

36 

28.98 

28.82 

28.55 

28.20 

27.75 

27.22 

26.63 

25.98 

25.24 

24.45 

23.59 

22.68 

21.72 

38 

30.60 

30.43 

30.15 

29.77 

29.32 

28.78 

28.18 

27.51 

26.77 

25.96 

25.10 

24.19 

23.22 

40 

32.24 

32.03 

31.73 

31.36 

30.89 

30.34 

29.72 

29.03 

28.29 

27.48 

26.62 

25.70 

24.73 


The values for density are given as cr^ values. Density at a pressure of one atmosphere, is obtained from the relation 

_ 1 ,000 at 
1 ,000 


CONl inEM I \i^ 


16 


PRACTICAL UNITS AND RELATIONS 


being greater at lower temperatures. It may be as- 
sumed to be independent of salinity within the salin- 
ity range encountered at sea. Since the ballast tanks 
are open to the sea, the water they contain is com- 
pressed equally with that which they displace. Only 
the pressure hull, which has a displacement of about 
3.6 X 10^ pounds resists compression. Consequently 
the buoyancy of a submarine is increased 14.2 x 10“^ x 
3.6 X 10^ = 512 pounds per 100 feet of increased depth 
as a result of the compression of the displaced sea 
water. 

Fuel oil ballast, however, has a compression about 
twice that of sea water. With increase in depth a small 
amount of sea water will enter the fuel ballast tanks 
and somewhat reduce the buoyancy. Taking the com- 
pression of fuel oil to be 2.8 x 10-^ per foot and its 
density to be 0.8 that of sea water it may be estimated 
that the buoyancy of a submarine is decreased 78 
pounds per 100 feet descent for each 100 tons of fuel 
oil carried. With a maximum load of 400 tons fuel oil, 
this effect will amount to about 300 pounds per 100 
feet. This effect cannot be estimated usefully since the 
quantity of fuel oil present is variable. 

The magnitude of the effect of compression of sea 
water in increasing buoyancy can only be rather 


roughly set at about 500 pounds per 100 feet descent 
because of the variable amounts of fuel oil carried. 

4 7 the coefficient of compression 

The coefficient of compression, C, expressing the 
combined effect on buoyancy of the compression of 
sea water and of the vessel with depth, is conveniently 
defined in relation to a change in depth of 100 feet. 
When so defined, it will be referred to as the compres- 
sion and is expressed as pounds per 100 feet. 

Compression = (ATT — VApts) 100/aZ. (1) 

For a fleet- type submarine of 2,400 tons submerged 
displacement. 

Compression = (ATT — 5.4 x lO^^Ap^s) 100/AZ. (2) 

Compression always has a negative value, since it rep- 
resents a loss of buoyancy with depth. The numerical 
value is frequently expressed without sign, the nega- 
tive character of the coefficient being understood. 

The term Diving Rule is used as a synonym for the 
compression. 


Chapter 5 

COMPRESSION 


W HEN A submarine dives its buoyancy changes 
for two reasons. As the hydrostatic pressure in- 
creases with depth the water becomes more dense be- 
cause it is compressed. It has been pointed out in 
Section 4.6 that this effect increases the buoyancy of 
a submerged submarine of 2,400 tons displacement by 
about 500 pounds per 100 feet. The hydrostatic pres- 
sure also compresses the hull of the submarine so that 
its displacement becomes less. This leads to a decrease 
in the buoyancy of the submarine. The net change in 
buoyancy which must be compensated for by adjust- 
ing the variable ballast is thus the difference between 
that required by the compression of the sea water and 
that resulting from the compression of the hull.^ 

It is possible to obtain a reasonably satisfactory 
estimate of the total change in buoyancy due to com- 
pression effects by observing the ballast change re- 
quired to maintain good trim on changing depth. If 
this estimate is corrected for the effect of changes in 
density of the water arising from temperature and 
salinity differences, the resulting figure may be taken 
to represent the compression resulting from the com- 
bined effect on the volume displacement of the hull 
and the compressibility of sea water. Since the latter 
is known approximately the true hull compression 
may be estimated if desired. For most practical pur- 
poses, however, it is the resultant effect of the simul- 
taneous compression of the hull and of the sea water 
which needs to be known. 

The coefficient of compression C is defined by equa- 
tion (1) Section 4.7 as: 

c = (ait - VApts) 100/AZ 


5 1 THE MEASUREMENT OF 

COMPRESSION 

In order to measure the compression of a subma- 
rine, the vessel is trimmed at periscope depth (keel 
depth about 60 feet) or in case of rough weather at 
the least depth practicable (usually 100 feet). The 
content of all variable ballast tanks is recorded and a 
sample of sea water is collected for the determination 
of its density. The submarine is then taken to the 
greatest depth practicable and trimmed and the same 
data are secured. Finally the submarine is trimmed 
near the surface and the required data recorded once 
more. 

The estimation of compression from data obtained 
in this way is illustrated in Table 1. 

Table 1. Data Illustrating the Estimation of Compression. 


Observations 

Depth 65 ft 

Temperature 57.5 F 

Density 1.0246 

Calculation 
Ballast Change (A IE) 

Depth Change (AZ) 

Density Change (Ap^g) 

Density Effect (5.4 X 10'’’Ap(g) 


265 ft 
53.0 F 
1.0250 


-2,000 lb 
200 ft 
+ 0.0004 
+ 2,160 lb 


65 ft 
58.0 F 
1.0246 


+ 1,500 lb 
-200 ft 
-0.0004 
-2,160 lb 


Descent 

Compression = (A IE — 5.4 X 10®Ap^g) 100 /a 2 
= (-2,000 - 2,160) 100/200 
= —2,080 pounds per 100 feet 

Ascent 

Compression = (+1,500 + 2,160) 100/-200 
= —1,830 pounds per 100 feet 


and the characteristic value of the compression of a 
fleet-type submarine is given, in pounds per 100 feet 
change in depth by: 

(ait - 5.4x10«Ap,,) 100/AZ 

where AZ is change in depth in feet. 

a The effect of the compression of fuel oil discussed in Section 
4.6 is difficult to take into account because of the different 
amounts of oil which will be present from time to time. Since it 
is not large it has been overlooked or neglected in most of the 
studies made to date. 


Mean compression for ascent and descent = —1,955 
pounds/100 feet. 

5.1.1 Measurement of Density of Sea Water 

Samples should be drawn from a water line open- 
ing immediately to the sea from the approximate 
level of the center of buoyancy of the submarine. 
Either the pressure gauge line in the forward torpedo 
room or the line supplying the officers’ head is suit- 
able. Lines drawn from ballast tanks or heated by 
machinery are unsuitable. 



17 


18 


COMPRESSION 


Density is most precisely determined by calculation 
from chemical analysis of salinity and measurements 
of the temperature of the water. The temperature 
should be taken immediately on collection and 
should be correct to 0.2 F. 

Satisfactory measurements of density may be made 
with a floating hydrometer provided care is taken 
to secure readings before the temperature of the water 
has changed. The presence of air bubbles adhering to 
the hydrometer must be scrupulously avoided. Suit- 
able hydrometers called “Marine Hydrometers” have 
been designed for this purpose.'^ Specific gravity hy- 
drometers designed for a range 1.02 to 1.03 may also 
be employed. These do not read the density, as de- 
fined in Section 4.2, correctly. The scale values of a 
specific gravity hydrometer is referred usually to the 
density of water at 60 F while that of a density hydro- 
meter is referred to water of 4 C. Differences in den- 
sity are, however, essentially the same as differences 
in specific gravity and the absolute values of the scale 
are consequently unimportant. 

If means of measuring the density of the water are 
not available, useful measurements of compression 
may be made by selecting a place where the water is 
thoroughly mixed so that density gradients are not 
present. The compression is then given directly by the 
amount of ballast pumped per 100 feet descent. If the 
temperature does not change more than 1 F per 200 
feet, it is probable that the salinity will also be uni- 
form and the density correction will be less than 500 
pounds per 100 feet which is about the limit of accur- 
acy of the procedure. Such conditions may be found 
in temperate latitudes during the winter and may 
also be found in many parts of the subtropical oceans 
at all seasons. 

If tests are made in fresh water the density may be 
obtained simply from a measure of temperature. The 
relation between temperature and density of fresh 
water may be obtained from Table 1 of Chapter 4, 
using the values of Salinity = 0. The relation differs 
significantly from that characteristic of salt water and 
consequently the curve shown in Figure 1, Chapter 2, 
should not be employed. 

Establishment of Trim 

In securing trim at each depth great care is re- 

b Manufactured by Nurnberg Thermometer Company, Inc., 
Brooklyn, New York, for the Bureau of Ships. 


quired. The speed of the vessel should not exceed 
40 turns or 2 knots and ballast should be adjusted so 
that constant depth is held with a hull angle less than 
1 degree and diving plane angles less than 5 degrees. 
It is possible to adjust ballast correctly to within 
about 500 pounds in this way. At speeds much greater 
than 2 knots, depth may be controlled with the planes 
when trim is far from perfect and the results of the 
test will be unsatisfactory. 

Trim should be established and observations made 
at two depths as far apart as possible so that the errors 
of measurement will be minimized when they are 
divided by the change in depth. When compression 
is determined during routine deep-submergence 
tests, in which it is customary to level off at a series 
of increasing depths, it is desirable to secure good 
trims and a measure of the density of the water at 
each depth. It is then possible to select the most fa- 
vorable levels for use in computing compression. 

It is undesirable to use data secured when the sub- 
marine lies in a strong density gradient. Under this 
circumstance the density of the water may vary 
greatly at the various depths occupied by the hull. A 
sample of water drawn under these conditions may 
not represent fairly the mean density of the layers 
in which the displacement lies. 

Venting Tanks 

Before a compression test is made all tanks should 
be carefully vented to remove the last traces of en- 
trapped air. Air bubbles are highly compressible and 
if they are carried down by the submarine the test 
will yield erroneously high values for compression. 
See Section 5.3 below. 

It is preferable that the vents be closed during the 
test so that the water enclosed in the main ballast 
tanks before descent will not be replaced in part by 
denser water into which the submarine may descend, 
since this would also lead to erroneously increased 
values for compression. 

Changes in Weight Due to Leakage 

Care should be taken that the weight of the vessel 
is not altered by factors which are not taken into ac- 
count such as pumping the bilges or the sanitary tank, 

c The relation of the vents to changes in the temperature of 
the ballast water and its effect on the buoyancy of a submarine 
are discussed in Chapter 7. 


)N 1 1 


THE COMPRESSION OF SUBMARINES 


19 


blowing safety tank, or flooding negative tank during 
the tests. 

Leakage is a very serious source of error, particu- 
larly when the tests are made on a new vessel during 
deep-submergence tests. New submarines frequently 
leak extensively and since the tests require several 
hours, the increase in weight may be very large. It is 
not uncommon for such a vessel to need to pump bal- 
last both on descent and ascent since the leakage may 
be greater than the ballast change required because 
of compression. 

Two procedures are available for dealing with the 
effects of leakage. One is to be sure that the bilges are 
pumped dry before each trim is established. The 
other is to assume that leakage is the same during de- 
scent and ascent and to average the values for the co- 
efficient of compression. 

Because of the likelihood of leakage it is preferable 
to make a special dive to maximum depth for the esti- 
mation of compression and to make it with as little 
delay as possible. 

5.1.5 Measurements of Ballast Changes 

The liquidometer gauges measuring the contents 
of the auxiliary ballast tanks are not very sensitive 
and may vary in their indication by as much as 500 
pounds when no change has been made in the con- 
tent of the tank. This is due in part to the effect of 
small changes in the angle at which the hull lies in 
the water. 

To minimize this source of error all ballast changes 
during a test should be made in a single tank, so that 
the errors in reading several gauges are not added. 
If changes in fore and aft trim are required they 
should be made by pumping from one tank to an- 
other rather than to and from the sea. 

The pump gauges installed in the earlier fleet-type 
submarines are very inaccurate. These gauges oper- 
ate by counting the pump strokes. Leakage of the 
valves causes the delivery to fall below the indica- 
tion. Pumps installed more recently appear to be 
more reliable and measure the water pumped more 
precisely than do the liquidometer gauges. These 
pumps, however, cannot be used to measure the 
amounts of ballast flooded. 

So long as ballast adjustments were made entirely 
by trial, accurate measurements of ballast changes 
were not necessary. If full advantage is to be taken of 
the improvement in precision of operation, which is 


possible with instruments for predicting ballast 
changes, improvements in the design of tanks and 
gauges are needed. 

5 2 the compression of submarines 
^•2-1 Results of Compression Tests 

Fleet-type submarines have yielded values for com- 
pression varying from 500 to 8,000 pounds per hun- 
dred feet. Beginning with the SS 285 commissioned in 
the spring of 1943, important changes in hull con- 
struction were introduced with a view to increasing 
the depth of safe operation. Submarines of earlier 
design will be referred to as light-hulled, and subse- 
quent construction as heavy-hulled vessels. Four sub- 
marines, SS 361-364, were modified only with regard 
to the weight of the frames, the plating being similar 
to that used in the earlier vessels. Table 2 shows the 
results of tests on 50 vessels, and is arranged to show 
the number of submarines of each type yielding vari- 
ous magnitudes of compression. 


Table 2. Compression of Fleet-type Submarines. 



Number 

Range of compression 

Average 

Type of 

of 

1,750- 2,500- 

compres- 

vessel 

tests 

<1,750 2,500 3,500 3,500 

sion 


Light hull 
(SS 212-284) 

25 

5 

6 

9 

5 

2,700 

Light hull— 

heavy frames 
(SS 361-364) 

4 


3 

0 

0 

2,000 

Heavy hull 
(SS 285 and 

SS 313 class) 

26 

13 

10 

3 

0 

1,700 


These tests make it clear that the compression var- 
ies with the hull construction. No differences were 
demonstrated between the products of different yards. 
Since the observations were made for the most part 
on new construction during deep-submergence tests 
it is probable that leakage and perhaps other causes, 
such as the inexperience of new crews, has led to un- 
due variation in the results and on the whole to val- 
ues which are too large. It is not probable that minor 
differences in design and construction are responsi- 
ble for the extreme differences observed among sub- 
marines of the same class. 

Information obtained at Pearl Harbor confirms 
the belief that tests with seasoned vessels and crews 


20 


COMPRESSION 


yield somewhat lower values for compression. The 
values for the compression of such vessels indicated 
by tests and patrol experience are given in Table 3. 


Table 3. Compression of Seasoned Submarines. 


Type of vessel 

Number of 
vessels 

Compression 
lb per 100 ft 

Light hull including 

2 

1,500 

T and Gato class 

8 

2,000-2,200 


2 

2,500-2,800 

Average: 

2,090 

Heavy hull Balao 

1 

1,700-1,900 

class 

10 

1,300-1,500 

Average: 

1,430 


Of the older types of submarine, controlled com- 
pression tests have only been made on the S-33 which 
yielded a value of 3,000 pounds per 100 feet. This 
vessel displaced 1,070 tons submerged. This compres- 
sion corresponds to 6,700 pounds per 100 feet for a 
vessel of 2,400 tons. 

Experience in diving has indicated that the com- 
pression of other old type submarines are about as 
given in Table 4. 


Table 4. Compressions of Older Type Submarines. 


Class 

Submerged 
displace- 
ment tons 

Number 

of 

vessels 

reported 

Compression 
lb per 100 ft 

Corresponding 
compression 
for 2,400 tons 

S (new) 

2,200 

5 

2,000-2,500 

2,200-2,700 

P 

2,000 

3 

2,500-3,000 

3,000-3,600 

S (old) 

1,100 

5 

1,100-2,700 

2,400-3,400 


Estimates have been made on the compression of 
four British submarines from data supplied by the 
British Admiralty delegation through courtesy of 
Captain (S) Third Submarine Flotilla, HMS Forth, 
and is recorded in Table 5. 


Table 5. Compressions of British Submarines. 


Vessel 

Submerged 

displacement 

tons 

Compression 
lb per 100 ft 

Corresponding 
compression 
for 2,400 tons 

Venturer 

800 

750 

2,250 

Viking 

800 

1,050 

3,500 

Stratagem 

1,000 

937 

2,250 

Spirit 

1,000 

900-1,000 

2,160-2,400 


These compressions agree in general with those re- 
ported for the older type of American submarines. 

Taken as a whole, the data indicate that slight im- 
provements in compressibility have been made with 
the development of the light-hulled fleet-type sub- 
marine. The new heavy-hulled fleet-type submarine 
is, however, distinctly improved in this respect. 

5.2.2 Variation in Compression of 
Individual Submarines 

The measurements of compression of fleet- type sub- 
marines summarized above show surprisingly wide 
variation. This variation is attributable in part to 
inaccuracies inherent in the method of making the 
tests and to faulty technique in carrying out the de- 
termination. The residue may result from real dif- 
ferences in the design and construction of the vessels 
and there is in addition the possibility that unrecog- 
nized factors are also contributory. 

Data are available from 19 submarines on which 
the compression has been estimated during two or 


Table 6. Selected Data on Compressibility of Submarines 
in Which Duplicate Tests Agree Within 500 Pounds per 
100 Feet. 


Vessel 

Mean 

compression 

Variation 

(Light 

hull) 

Puffer* 

1,900 

±300 

Pargo* 

3,150 

±350 

Bluefish* 

3,300 

±300 

Cod* 

2,900 

±500 

Darter* 

3,300 

±100 

Golet 

2,300 

±100 

Cobia 

2,300 

±300 

Class Average 

2,730 


Average of extreme 

mean values 

2,600 

±700 

(Heavy 

hull) 

Cisco* 

1,550 

±150 

Apogon* 

1,880 

±500 

Aspro* 

2,250 

±350 

Pintado* 

900 

±100 

Dragon ET 

1,300 

±380 

Redfish 

1,450 

±350 

Class Average 

1,540 


Average of extreme 

mean values 

1,575 

±675 


* These check dives were made on same test cruise. 


EFFECT OF ENTRAPPED AIR ON APPARENT COMPRESSION 


21 


more separate dives. Thirteen of these, which show 
agreement on successive tests within ± 500 pounds of 
their mean, are recorded in Table 6. This agreement 
is as good as can be expected, considering errors in 
reading ballast tank liquidometer gauges and in se- 
curing trim at low speed. Measurements influenced 
by faulty technique in securing trim or otherwise 
handling the vessel are probably excluded. 

Table 6 shows that the average compression of the 
selected light-hulled submarines is 2,730 pounds per 
100 feet. The extreme values of mean compression 
for individual vessels fall within ± 700 pounds of 
their average of 2,600. For the heavy-hulled subma- 
rines the average compression is 1,540 pounds per 100 
feet. The extreme values of mean compression for in- 
dividual vessels fall within ± 675 pounds of their 
average of 1,575. 

The result confirms the conclusion that a real dif- 
ference exists between the compression of submarines 
of different design and construction. The variation 
between different vessels of the same class is large 
enough to suggest that there may be some real dif- 
ference in their compressibility, but a larger series of 
measurements is required to demonstrate this point. 

5.2.3 True Compressibility of 

Submarine Hulls 

Compression tests measure the combined effects 
of hydrostatic pressure on the displacement of the 
hull and on the density of the displaced sea water. 
Since the compressibility of sea water is known and 
increases the buoyancy of a submerged submarine of 
2,400 tons displacement by about 500 pounds per 
100 feet, it is necessary only to add this amount to the 
measured compression to obtain an indication of the 
actual change in displacement of the submarine. 

Thus one of the older light-hulled type submarines 
with a measured compression of 2,700 pounds per 100 
feet actually undergoes a change in displacement of 
about 3,200 pounds and a modern heavy-hulled ves- 
sel with a compression of 1,400 pounds displaces 
about 1,900 pounds less on descending 100 feet. Im- 
provements in design have almost doubled the rig- 
idity of submarine hulls. Further improvements in 
like degree would reduce the true hull compression 
until it is nearly equal to the compressibility of sea 
water. If this could be accomplished submarines 
would never need to pump ballast on descent, and 
whenever density gradients were present they could 


float balanced in the gradient without depending on 
propulsive machinery to maintain their proper depth. 

Improvements in design intended to permit greater 
range in depth and improved resistance to depth 
charges may thus also increase the ease of underwater 
operation. 

Batten Measurements 

A direct indication of the effect of compression 
with depth on the displacement of a submarine’s hull 
is given by measurements of the change in diameter 
of the pressure hull on deep submergence. These 
measurements, made with steel battens secured to 
brackets welded to the pressure hull frames, are cus- 
tomarily made in both the vertical and horizontal 
direction in the seven compartments of the hull dur- 
ing precommissioning trials. 

Data secured by the Supervisor of Shipbuilding, 
U.S.N., at Manitowoc, Wisconsin, during deep- 
submergence tests of 22 submarines of new construc- 
tion, indicate that the average decrease in diameter 
of the pressure hull is 0.0295 inch per 100 feet de- 
scent in the case of light-hulled vessels and 0.0275 
inch per 100 feet descent in the case of the heavy- 
hulled submarines of later design. These changes 
in diameter are estimated to lead to a decrease in dis- 
placement of 1,650 and 1,540 pounds per 100 feet 
respectively. 

These estimates of the true compressibility of the 
submarine hulls are notably lower than those based 
on ballast changes required during deep submerg- 
ence, which are 3,200 and 1,900 pounds per 100 feet 
respectively for the two types of construction. The 
difference may be attributed in part to the compres- 
sion of fuel oil and entrapped air since these factors 
lead to excessive values in the compression tests. 
More important, the batten measurements do not 
record the bending of the plates between frames, and 
consequently give too small a value for the change 
in displacement of the pressure hull. 

5 3 EFFECT OF ENTRAPPED AIR ON 
APPARENT COMPRESSION 

Any large volume of air entrapped in a fuel or bal- 
last tank or in any other place where it is exposed 
to the pressure of the sea will be compressed when 
the submarine descends and will cause an undue loss 
of buoyancy. If such a condition exists during a com- 


22 


COMPRESSION 


pression test, abnormally high values for compression 
will result. It is believed that when compression mea- 
surements yield results more than 1,000 pounds in ex- 
cess of the mean value for boats of the class, air is 
present. It is suspected that smaller departures from 
the mean compression may frequently be due to the 
accidental entrapment of smaller quantities of air. 

In the construction of a submarine, every effort is 
made to eliminate air pockets and, if vent holes are 
cut in accordance with the detailed working plans, 
there should be a negligible amount of air trapped 
in the tanks or in the outside structure. However, 
it sometimes happens that sections of the superstruc- 
ture are not adequately provided with vent holes dur- 
ing construction and these pockets are uncovered in 
service if the volume is sizable enough to cause erratic 
performance in diving. In the absence of pockets of 
this type, there is always the possibility that the tanks 
are not properly vented to eliminate all the air possi- 
ble. 

The presence of entrapped air reveals itself in the 
way in which buoyancy decreases with depth. Nor- 
mally, as the result of compression, the volume dis- 
placement of the vessel decreases in direct proportion 
to the depth. On the other hand, since pressure in- 
creases with depth, the volume displacement of an en- 
trapped air bubble is the reciprocal of the depth, 
since the volume of a gas is inversely proportional 
to its pressure. As a result, the net buoyancy of a ves- 
sel carrying a large volume of entrapped air decreases 
very rapidly at the beginning of its descent but less 
and less rapidly as depth increases. The estimated 
compression of the vessel, which represents the sum of 
the true compression^’ and the compression of the air 
bubble, will consequently diminish when measured 
between successively deeper levels. 

A bubble having a volume at sea level equal to the 
displacement of 1,000 pounds of sea water® has an 
effect on the buoyancy of a submarine at any keel 

depth which is given by the term j p(>tmds, 

'IF 

where D is the keel depth in feet, it being assumed 
that the bubble is centered 15 feet above the keel. The 
form of this relation is illustrated in Figure 1. It is 



KEEL DEPTH -FEET 

Figure 1. Effect of a volume of entrapped air, which at 
atmospheric pressure displaces 1,000 lb of sea water, on 
the buoyancy of a submarine at various keel depths. 

evident from this figure that the greater part of the 
loss of buoyancy from the compression of the air will 
occur between the surface and 100 feet depth and 
that below 200 feet the effect of further compression 
of the air is relatively small. 

The size of an entrapped air bubble may be de- 
termined approximately with the aid of Figure 1 if 
hydrographic conditions and the compression of the 
submarine are known or may be reasonably assumed. 
If the displacements of a quantity of air which dis- 
places 1,000 pounds of sea water at the surface are 
represented by and Vo at the depth and at some 
greater depth Zo, then the displacement at the surface 
is given by^ 


ATF- C(Z2 - Z,)/100 - 

Vo - Fi 


X 1 ,000 pounds. 


( 1 ) 


and the volume of gas at 1 atmosphere pressure is 
given by 


ATF- C{Zo - Zi)/100 - V/\pt, 

V2- Vi 


X 15.6 cu ft. 


( 2 ) 


d The true compression here refers to the combined effect of 
compression of the hull and compression of sea water. 

e 1,000 pounds of water are displaced by 15.6 cubic feet or 1 18 
gallons. 


f In these expressions in accordance with definitions pre- 
viously given AIF = change in ballast between depths Zj and 
Z.,; C = change in buoyancy due to compression per 100 feet in- 
crease in depth; V = submerged displacement of submarine in 
pounds; Apf^ = change in density of sea water between depths 
and Z^. 



EFFECT OF ENTRAPPED AIR ON APPARENT COMPRESSION 


23 


The pressure and size of an unsuspected bubble of 
entrapped air is indicated by the data in Table 7 se- 
cured during a dive of a British submarine of 1,000 
tons displacement. The first part of the table shows 
the data obtained at several levels between 30 and 


Table 7. Apparent Compression of the 1,000 -ton Sub- 
marine, HMS Spirit Suspected of Carrying Entrapped air. 


Depth 

Change in buoyancy due to 

Change Density Apparent 

in of sea compres- 

ballast water sion 

Estimated 

compres- 

sion 

lb/100 ft 

30 

0 

0 0 

- 

100 

-1,250 

+ 2,240 -3,490 

4,986 

200 

-2,500 

+ 3,360 -5,860 

2,370 

300 

-3,400 

+ 3,360 -6,760 

900 

Estimation of Displacement of Air Assuming Compression 

of- 

1,100 Pounds per 100 Feet, 



Change in buoyancy due to 




1,000- 

Estimated 


Apparent 

Assumed Assumed pound 

displace- 


compres- 

compres- air air 

ment 

Depth 

sion 

sion bubble bubble 

of air 

30 

0 

0 0 0 

— 

100 

—3,490 

—770 —2,720 —400 

6,800 

200 

—5,860 

—1,870 —3,990 —530 

7,528 

300 

—6,760 

—2,970 —3,810 —580 

6,570 


300 feet from which the compression is estimated be- 
tween each descending pair of levels. The apparent 
compression represents the change in buoyancy of 
the vessel due to compression in descending from 30 
feet to the stated depth, estimated from the ballast 
change and the change in density of the sea water. 
The estimated compression shows the compression 
per 100 feet between each stated depth. It is evident 
that the compression is much greater at the upper 
levels than between deeper levels, which indicates 
that entrapped air is present. In the second part of 
the table, the displacement of the air is estimated 
from the change in buoyancy between 30 feet and 
each greater depth. This is done by estimating the 
change in buoyancy due to the actual compression of 
the hull, assuming a reasonable value ( — 1 , 1 00 pounds 
per 100 feet) for the buoyancy due to compression 
(column 3). The difference between change due to the 
apparent compression and the assumed compression, 
gives the change in buoyancy due to the assumed air 
bubble (column 4). The change in buoyancy of a 


1,000-pound air bubble at each stated depth is then 
obtained from Figure 1 and entered in column 5. By 
comparing the change in buoyancy of the assumed air 
bubble and the 1,000-pound air bubble, the displace- 
ment of the air is obtained (column 6). The results 
indicate that the air displaces about 7,000 pounds 
corresponding to 109 cubic feet when at the surface. 

In this case, the compression of the submarine was 
unknown. The apparent compression between 200 
and 300 feet suggested the proper order of magnitude 
and trials were made with various compressions until 
the most uniform values for the displacement of the 
air were obtained. This is obviously not a satisfactory 
method of determining compression. When the re- 
sults of compression tests indicate the presence of en- 
trapped air, the condition should be remedied and 
the test repeated under more favorable circumstances. 

Definite evidence of the effects of entrapped air 
were obtained during the deep-submergence test of 
the USS Flounder. Immediately prior to the test a 
trim dive was made in order to weigh the vessel. From 
the ballast adjustments required to trim the sub- 
merged vessel, it was estimated that a large amount of 
air was present in one of the after fuel tanks. The size 
of this bubble was estimated to be 700 to 800 cubic 
feet at periscope depth, corresponding to 1,800 to 
2,000 cubic feet at the surface. 

Table 8. Apparent Compression of the 2,400-ton Sub- 
marine USS Flounder (SS 251) Carrying Entrapped Air. 


Change in buoyancy due to 


Depth 

Change 

in 

ballast 

Density 
of sea 

water 

Apparent 

compres- 

sion 

Estimated 

compres- 

sion 

lb/ 100 ft 

90 

0 

0 

0 

— 

162 

-9,500 

+ 50 

-9,500 

13,200 

212 

-12,800 

+ 320 

-13,120 

7,240 

312 

-13,400 

+4,260 

-17,660 

4,540 


Estimated Displacement of Air Assuming Compression of 
2,600 Pounds Characteristic of Class. 


Change in buoyancy due to 


Depth 

Apparent 

compres- 

sion 

Assumed 

compres- 

sion 

Compres- 
sion 
of air 

1,000- 

pound 

air 

bubble 

Estimated 

displace- 

ment 

of air 

90 

0 

0 

0 

0 

— 

162 

—9,500 

—1,870 

—7,630 

—120 

63,600 

212 

—13,120 

—3,170 

—9,950 

—155 

64,110 

312 

—17,660 

—5,770 

—11,890 

—185 

64,400 


24 


COMPRESSION 


Following the trim dive, the Flounder made a 
deep-submergence test in the course of which the 
data recorded in Table 8 were secured, and the dis- 
placement of the entrapped air estimated as ex- 
plained in discussing the data obtained by the HMS 
Spirit. 

The change in ballast required to compensate for 
compression was unusually large and the estimated 
compression is much greater between levels near the 
surface than between deeper levels. When the dis- 
placement of the air is estimated, assuming a com- 
pression for the Flounder of —2,600 pounds per 100 
feet, which is the average value for her class, a value of 
about 64,000 pounds or 1,000 cubic feet at one atmos- 
phere pressure was obtained. 

On return to the yard. Number 6 A and 6B Fuel 
Tanks were found to be only about one-quarter full, 
verifying the existence of an air bubble. From the 
content of the tank, it was estimated that the volume 
of air was about 900 cubic feet. Comparing the re- 
sults of the three methods of estimation, the volume 
of air was as follows: 

Weighing boat .... 1,800 to 2,000 cubic feet 

Compression test 1,000 cubic feet 

Direct observation 900 cubic feet 


where L = distance measured aft of center of buoy- 
ancy; 

dp = distance of forward trim tank from center of 
buoyancy; 

= distance of aft trim tank from center of buoy- 
ancy, and where between any two depths; 

AWp = change in ballast in forward trim tank; 

AW A = change in ballast in aft trim tank; 

AD = change in displacement of entrapped air. 

A negative value of L indicates air entrapped forward 
of the center of buoyancy. 

In the case of the observations on the USS 
Flounder on descending from 90 feet to 312 feet: 

AWp = -f 900 pounds 

AWa = — 5,500 pounds 

AD = — 11,890 pounds 


The location of the entrapped air should be indi- 
cated approximately from the change in fore and aft 
trim required on descent if the displacement of the 
air is known. If the air is entrapped at some distance 
aft of the center of buoyancy, for example, its com- 
pression will cause the submarine to become heavy 
aft and an appropriate amount of ballast must be 
tranferred forward to compensate. The quantity of 
ballast shifted will depend on the change in displace- 
ment of the air and the ratio of the distances of the 
bubble and of the fore and aft tanks from the center 
of buoyancy. 

The approximate position of the entrapped air 
should be indicated by L in the equation: 

L = — dp AWp 


dp = 120 feet 

dA= 140 feet 

1 he distance of the air aft of the center of buoy- 
ancy, L, comes out to be 73.8 feet. Tanks 6A and 6B, 
in which the air was located, center 44 feet aft of the 
center of buoyancy. The agreement is not very satis- 
factory and indicates that the position of the bubble 
can be determined only in a very general way by such 
estimations. 

Submarines are sensitive to small changes in fore 
and aft trim since a change of only 200 pounds causes 
a change in hull angle of 1 degree. Whenever a sub- 
marine becomes unexpectedly heavy at one end on 
changing depth the possible presence of entrapped 
air should be considered. 


Chapter 6 

THE PREDICTION OF BUOYANCY CHANGES DUE TO 
DENSITY GRADIENTS IN THE SEA 


M easurements of density of sea water obtained by 
the use of hydrometers or by chemical analyses 
for salinity and from temperature readings take too 
long to be a useful guide to actual diving operations. 
A continuous and instantaneous indication of the 
density of sea water, preferably in the form of a 
graphic record of its effect on buoyancy with chang- 
ing depth, is needed to provide useful information 
to the diving officer as the vessel moves from one 
depth to another. 

6 1 SUBMARINE BATHYTHERMOGRAPH 

The type CTB submarine bathythermograph 
[BT],*^ an instrument designed originally for use in 


a Abbreviation for bathythermograph. See note a, Chapter 1, 


sonar predictions, provides this information in so far 
as density gradients due to temperature differences in 
the water are concerned. Since temperature differ- 
ences are the principal source of density layers in most 
parts of the ocean, this instrument has proved of im- 
mediate value as a guide to diving operations. The 
OCN and OCO are more recently developed tempera- 
ture-depth recorders intended to improve on the type 
CTB bathythermograph in various ways. The model 
CXJC is an instrument which takes account of den- 
sity effects due to salinity as well as temperature. 

The type CTB submarine bathythermograph draws 
a curve on a smoked card as the submarine dives. The 
principle of operation is evident from Figure 1. The 
card carriage is rotated about a pivot by a Bourdon 
tube actuated by the sea pressure. The upward move- 
ment of the card holder during descent causes the 



25 


26 


PREDICTION OF BUOYANCY CHANGES 



Figure 2. Type CTB bathythermograph installed. 


writing point to trace a descending line on the 
smoked card, proportional in length to the increase 
in depth. The writing point is mounted on an arm 
which rotates in a horizontal plane under the action 
of a second Bourdon tube connected with a tempera- 
ture sensitive element exposed to the sea, usually at 
the level of the conning tower. The rotation of the 
arm causes the writing point to deflect the tracing to 
the right or left, a distance proportional to the change 
in temperature. Figure 2 pictures the instrument and 
Figure 3 illustrates the chart. 

The model OCN bathythermograph is a similar 
instrument designed with the special needs of the div- 
ing officer in mind. The shape of the instrument has 
been modified to provide for more convenient mount- 
ing on the panel carrying the depth gauges and other 
instruments used in diving. The size of the chart has 



Figure 3. Smoked chart used in type CTB bathythermo- 
graph, showing simidated temperature trace. Reduced to 
y- natural size. 


been increased so that the record can be read by the 
diving officer while standing at his station. These 
changes have involved complete redesign of the 
mechanical arrangements, but in principle it differs 
in no way from the CTB model. The model OCN 
bathythermograph is pictured in Figures 4 and 5 and 
the chart is shown in Figure 6. The model OCN is 
now receiving test in service. 

The model OCO bathythermograph, like the 
models CTB and OCN, also records temperature and 
depth but employs electrical methods of recording. 
Temperature is measured by a thermocouple which 
generates a voltage in an electrical circuit. This volt- 
age is measured by means of a potentiometer circuit 
in the recorder, located in the control room, and is 
plotted on the vertical scale of the recorder in degrees 
of temperature. Depth is measured by sea pressure 
acting on a bellows connected with a slide-wire which 
is one arm of a Wheatstone bridge, the other arm of 
the bridge being in the recorder. Depth is plotted on 
the horizontal scale in the recorder. The depth-tem- 
perature curve is written in ink on a chart which is 
7x10 inches in dimensions. There are three separate 
thermocouples which are installed at the bow, on the 
periscope shears, and just above the bilge keel. Any 
one of these thermocouples can be thrown into the 



Figure 4. Model OCN bathythermograph installed in the 
control room. The cover has been opened and smoke re- 
moved from lower portion of the card to show the chart 
more clearly. 




SUBMARINE BATHYTHERMOGRAPH 


27 



Figure 5. Temperature-sensitive element of model OC.N 
bathythermograidi installed on the periscope shears. 

circuit means of a switch on the recorder, d he 
OCO recorder is shown in Figure 7, and the thermo- 
couple in Figure 8. 

^ The Interpretation of the 

Bathythermograph Record 

The tracing drawn by the instrument is a descrip- 
tion of the distribution of temperature with depth. 
In order to make use of this information in estimat- 
ing the ballast adjustment recpiired on changing 



Fu;ure 6. Chart used in model OCX hathythermograph. 
Reduced to 2/5 natural size. 


depth, it is necessary to provide some means of show- 
ing the change in buoyancy which will result from 
the change in temperature. It is also necessary at the 
same time to take account of the change in buoyancy 
which results from the compression due to increasing 
depth. 

I'his is done by adding to the bathythermograph 
chart a third set of coordinates which are sloped so 
that each passes through all the points where the loss 
in buoyancy with depth from compression is exactly 
etpial to the gain in buoyancy due to a decrease in 
temperature. If the temperature of the water varies 
with depth as shown by such a line then no change in 
ballast is required on changing depth. Such lines are 
consequently called isoballast lines. 





Figure?. Model OCO hathythermograph installed in the 
control room. 



Figure 8. Thermocouple of the Model OCO hathy- 
thermograjdi installed at the level of the hilge keel. 



28 


PREDICTION OF BUOYANCY CHANGES 


DEGREES FAHRENHEIT 

30 40 50 60 70 80 90 



Figure 9. Method of constructing grid of isoballast lines 
on a bathythermograph chart. The example is for a sub- 
marine with compression of 2,500 lb per hundred feet. 


DEGREES FAHRENHEIT 



Figure 10. Example of temperature trace which follows 
an isoballast line, in which case no change in buoyancy 
occurs on changing depth. 


The isoballast lines are spaced so that the interval 
between successive lines corresponds to a change in 
buoyancy of some fixed amount, conveniently 2,000 
pounds. It follows that when the temperature trace 
crosses the isoballast lines between any two depths, 
the change in buoyancy is given directly by the num- 
ber of isoballast-line intervals crossed. The ballast 
change required to compensate for the change in 
buoyancy may consequently be read off directly from 
the record. 

The methqd of constructing isoballast lines will 
make this clearer. From a curve such as Figure 1 in 
Chapter 1, showing the relation between temperature 
and the relative buoyancy of a submarine, a table is 
constructed giving a series of temperatures each of 
which corresponds to a buoyancy 2,000 pounds less 
than the preceding. Such a series, appropriate to a 
submarine of 2,400 tons submerged displacement, is 
entered in Table 1. 


Table 1. A Series of Temperatures for Use in Plotting 
Isoballast Lines for Submarines of 2,400 Tons Submerged 
Displacement. 


Each increment in temperature 
in buoyancy of 2,000 pounds. 

corre.'^ 

;ponds to a change 

32.0 

56.9 

70.5 

81.5 

40.0 

59.9 

72.8 

83.7 

45.3 

62.8 

75.0 

85.8 

49.6 

65.6 

77.2 

87.9 

53.2 

68.1 

79.4 

90.0 


The interval of depth which causes the buoyancy 
of the submarine to change by 2,000 pounds is next 
estimated from the relation: 

Depth interval = x 100 feet 

Lj 


where C is the compression of the submarine for 
which the chart is intended. The depth intervals for 
various compressions for which isoballast lines have 


been issued are as follows: 


Compression 

Depth intervals 

(lb per 100 ft) 

(ft) 

1,400 

143 

2,000 

100 

2,500 

80 

3,000 

66.6 

4,000 

50 


The temperatures corresponding to 2,000-pound 
increments in buoyancy, from Table 1, are marked off 
on the chart along the coordinate corresponding to 
the surface and again at the successive intervals of 
depth which each correspond to a 2,000-pound in- 
crement in buoyancy, as determined by the compres- 
sion of the submarine for which the chart is intended. 
Figure 9 illustrates the procedure in the case of a sub- 
marine with a compression of 2,500 pounds for which 
the depth interval is 80 feet. 

Sloping lines are drawn from each point on the 
surface coordinate to the next point to the left on the 
marked depth coordinate below, and continued simi- 
larly to the greatest depth represented. These lines 
are curved because the relation between temperature 
and buoyancy is not linear. 

It is evident from Figure 9 that each line is drawn 
through all the points in which the decrease in buoy- 
ancy due to compression with depth is exactly bal- 
anced by the increase in buoyancy due to the de- 
crease in temperature. Each line thus represents the 
conditions in which no change in ballast is required. 


SUBMARINE BATHYTHERMOGRAPH 


29 


DEGREES FAHRENHEIT 



Figure 11. Example of temperature trace which crosses 

the isoballast lines from left to right on descent, in which 

case buoyancy decreases on increasing depth. 

Thus if the temperature trace passes through the 
points A and B in Figure 10, a submarine in trim at 
A will lose 4,000 pounds buoyancy as the result of its 
compression in descending to B but will gain 4,000 
pounds buoyancy as the result of the decreased tem- 
perature of the displaced water at B. No change in 
ballast is required. 

It is also evident that if the temperature trace does 
not follow (or parallel) an isoballast line as in Figures 
11 and 12, the buoyancy of the vessel will change on 
descent to a degree which is indicated by the isobal- 
last line grid. Thus if the temperature does not 
change in descent, as from C to D in Figure 11, buoy- 
ancy is decreased 4,000 pounds because of compres- 
sion. This is indicated by the tracing crossing two 
isoballast-line intervals. On the other hand, if the 
temperature decreases markedly on descent as from E 
to F in Figure 12, buoyancy is increased 6,000 pounds 
as the result of the temperature change while it is de- 
creased 4,000 pounds by the compression. The result 
is an increase in net buoyancy of 2,000 pounds which 
is indicated directly by the fact that point F lies one 
isoballast-line interval to the left of point E. Conse- 
quently 2,000 pounds of ballast must be flooded in to 
preserve the trim which existed at E. 

The following rules are sufficient to interpret the 
BT chart in making trim adjustments in diving. 

1. If the temperature tracing crosses the isoballast 
lines from left to right during descent, the boat be- 
comes heavier and ballast must be pumped out to 
obtain good trim. On ascent, it must be flooded in. 

2. If it crosses the isoballast lines from right to left 
during descent, ballast must be flooded in to obtain 
good trim. On ascent, it must be pumped out. 

3. If it is parallel to the isoballast lines, no change 



Figure 12. Example of temperature trace which crosses 
isoballast lines from right to left in descent, in which case 
buoyancy increases on increasing depth. 


in ballast is required in moving from one depth to 
another. 

4. The ballast change required in moving between 
two depths is given by multiplying the number of 
isoballast-line intervals crossed by the temperature 
tracing between these depths by 2,000 pounds. How- 
ever, intervals crossed twice in opposite directions are 
not counted. 

Graphical Analysis of Buoyancy 
Problems 

The BT chart with isoballast lines provides a con- 
venient means for the graphical analysis of buoyancy 
problems. It is consequently desirable to relate the 
fundamental buoyancy equations outlined in Chap- 
ter 3 to their graphical representation on the BT 
chart. 

Equation (4) (Section 3.2) for change in net buoy- 
ancy, AB, is: 

AB — V/\pfg -j- C — A IT. 

Since the instrument does not take account of salinity 
changes, the term VApt is u.sed in place of V A pts to 
express buoyancy effects due to the temperature 
changes of the sea water. The terms of the equation 
may be expressed graphically by horizontal distances 
across the chart as shown in Figure 13. Their magni- 
tude is measured in units of 2,000 pounds by the num- 
ber of isoballast-line intervals crossed in the given 
distance. Thus if a submarine in trim at point A 
(depth Zi and temperature Ti) descends to point B 
(depth Z 2 and temperature and if D is the point 
at depth Z 2 on the isoballast line which passes 


30 


PREDICTION OF BUOYANCY CHANGES 


Tz T, 



Figure 13. GrajDhical representation of factors affecting 
buoyancy with the aid of temperature trace drawn on 
isoballast line grid. 


Tz T, 



Figure 14. Use of graphical method to determine depth 
at which a submarine may come to trim when ballast is 
flooded in. 


through the point of trim A, then VApt is repre- 
sented by the distance CB which corresponds to the 
decrease in temperature, and CaZ is represented by 
the distance DC which corresponds to the tempera- 
ture change required to counterbalance the compres- 
sion. This is the result of the way in which the iso- 
ballast lines are constructed. CaZ has a negative 
value since it represents a loss in buoyancy. 

The distance BD, equal to V Apt + CaZ, repre- 
sents the sum AB AW. If ATT = 0, i.e., if no bal- 
last adjustment is made, BD = AB and represents 
the change in net buoyancy resulting from the change 
in depth. If it is desired that AB = 0 at the depth Z 2 
then ballast must be added until AIT = BD. BD ob- 
viously represents the number of isoballast-line inter- 
vals crossed by the temperature trace between the 
depths Zj and Z 2 . 

The chart may be used not only to estimate 
changes in buoyancy, or required changes in ballast, 
in moving between two stated depths as illustrated 
above but also to show what may be expected to hap- 
pen in a variety of other circumstances. 

For example, suppose a submarine in trim at point 
A in Figure 14 floods an amount of ballast AIT while 
at the original depth Zj. The state of the vessel will 
be represented by the point E and it will be heavy by 
the amount A IT, measured in isoballast-line inter- 
vals, which will cause it to sink. The question is at 


what depth, if any, it will come to trim with neutral 
buoyancy. The state of the vessel as it sinks is repre- 
sented by the points along the isoballast line drawn 
through points E and B. At each depth this sloping 
line represents the temperature change required to 
compensate for the decreasing buoyancy due to com- 
pression in addition to the initial change in weight. 
If at some depth the temperature trace crosses this 
isoballast line, as at B, then at that depth the increase 
in buoyancy due to the temperature gradient will 
equal the decrease in buoyancy due to the added 
weight plus that due to compression and the subma- 
rine will again be in trim at that depth. If the sub- 
marine is caused to descend deeper, as to Bj, the loss 
in buoyancy represented by the continued course of 
the isoballast line drawn through B and E will be 
less than the gain in buoyancy represented by the 
temperature trace. The submarine will become light 
and must flood more ballast or decrease its depth if it 
is to come into trim. 

Selection of Correct Bathythermograph 
Card 

The isoballast lines each represent the locus of all 
points where the effect of temperature on buoyancy 
is equal and opposite to the effect of compression on 
buoyancy. The spacing of the lines with respect to 


PRECISION OF BATHYTHERMOGRAPH PREDICTIONS 


31 


temperature depends upon the displacement of the 
submarine; the spacing with respect to depth depends 
on the actual compression of the vessel and this varies, 
as shown in the preceding chapter, not only from one 
class of submarines to another, but also from one 
boat to another within a given class. It is conse- 
quently essential that BT cards be used with isobal- 
last lines appropriate to the displacement and com- 
pression of the submarine. 

Bathythermograph cards have been prepared for 
submarines of 2,400 tons submerged displacement 
having compressions of 1,400, 2,000, 3,000, 4,000, 
6,000 pounds per 100 feet. By selecting a card for a 
compression nearest to that of the submarine, errors 
in ballast estimates larger than 500 pounds per 100 
feet are avoided. The 1,400-pound card is recom- 
mended for the SS 285 and subsequent submarines, 
the 2,000-pound card for earlier fleet-type subma- 
rines, unless experience shows a different card is re- 
quired. It is believed that compression estimates 
greater than 3,000 pounds per 100 feet are usually the 
result of entrapped air, and will not be encountered 
in properly conditioned submarines. The cards for 
4,000- and 6,000-pound compressions are conse- 
quently being withdrawn from distribution. 

6 2 PRECISION OF BATHYTHERMOGRAPH 
PREDICTIONS 

The several factors which determine the precision 
of predictions of ballast change by the bathythermo- 
graph are enumerated below. 

Buoyancy as a Function of 
Temperature 

Temperature changes are recorded and may be 
read easily to about 0.5 C corresponding to buoyancy 
changes of about 150 to 450 pounds depending on the 
temperature. It is not easy to interpolate in reading 
isoballast-line intervals to less than 500 pounds. Fre- 
quently the zero setting of the temperature record- 
ing mechanism is wrong by several degrees. This does 
not introduce serious error since temperature differ- 
ences only are involved. 

The response of the thermal recording system is 
sufficiently quick, in relation to the speed of descent 
or ascent, that hysteresis is not present in the record 
provided the instrument is properly adjusted. Occa- 
sionally marked hysteresis is produced by excessive 


pen pressure, by bending of the copper tube which 
transmits the temperature effect, or by mechanical 
interference within the recorder. 

The numerical relation of temperature to density 
used in constructing isoballast lines is known with 
great precision. The displacement of fleet-type sub- 
marines agrees with that assumed in the calculations 
to 4 per cent at least. Repeated experience of tech- 
nicians, in observing the effect of shifting known 
quantities of ballast on the depth assumed by sub- 
marines balanced in strong temperature gradients, 
has conhrmed the reliability of estimates of buoyancy 
change due to temperature. 

Serious errors in estimating the proper compensa- 
tion for temperature changes may arise, particularly 
if abrupt temperature gradients are encountered, be- 
cause of the location of the blister housing the tem- 
perature sensitive element. The blister has usually 
been mounted on the conning tower fairwater, some 
15 or 20 feet above the center of buoyancy. Conse- 
quently it does not record the temperature of the 
water which is displaced by the greater part of the 
hull, and which determines its buoyancy. This diffi- 
culty is being reduced in recent experimental installa- 
tions by mounting the thermal element at the level 
of the bilge keel. 

Buoyancy as a Function of Salinity 

The BT does not take account of salinity gradients 
and may be significantly in error if they are present. 
This is the most serious source of error in the instru- 
ment. As discussed in Chapter 2 many parts of the 
ocean are free of substantial salinity gradients, and if 
they are present, some allowances for these effects may 
be made with the aid of the Submarine Supplements 
to the Sailing Directions described in Chapter 11. 

Buoyancy as a Function of Depth 

The BT reading of depth usually checks the depth 
gauge reading to within 5 feet. No serious error arises 
on this account except that occasioned by the location 
of the blister remote from the center of buoyancy. 
The determination of compression of individual ves- 
sels with precision is difficult. Experience indicates 
that individual submarines of a given class do not 
usually differ very much, and that better results are 
obtained by using an isoballast-line grid designed for 
the class, than using a special grid for each vessel. 


32 


PREDICTION OF BUOYANCY CHANGES 


Unfortunately several of the submarines first tested 
for compression gave abnormally high values, pre- 
sumably because of entrapped air, and this led to the 
belief that submarines varied in compression more 
than they do in fact. Consequently, cards were issued 
covering a greater range of compressions than are 
necessary and this in turn led to many submarines 
receiving and using the wrong card. Standard prac- 
tice now provides cards for compressions of 1,400, 
2,000 and 3,000 pounds per 100 feet. With proper se- 
lection errors in estimates of changes in buoyancy 
with depth should not exceed 500 pounds per 100 
feet. 

Buoyancy as a Function of Weight 

The predicted buoyancy change can only be 
checked, in practice, against the ballast change re- 
quired in restoring trim after a change in depth. 
Errors in estimating the ballast change arise from the 
inaccuracies of the gauges with which ballast water 
is measured. As pointed out in Chapter 5 these may 
frequently amount to 500 pounds or more. Errors 
also arise from the difficulty in determining when net 
buoyancy is zero. These errors apply to both the 
initial trim and that finally achieved after a change 
in depth. Even with great care, departures from zero 
buoyancy of less than 500 pounds cannot be easily 
recognized. Unless the submarine is balanced or is 
moving very slowly, the planing forces discussed in 
Chapter 9 may conceal the presence of a net buoy- 
ancy of 1,000 pounds or more. 

It is consequently believed that, unless substantial 
salinity gradients are present, the bathythermograph 
predictions are about as accurate as can be taken ad- 
vantage of in view of the inaccuracy of the tank 
gauges and the trimming operations. 

6.2.5 Adequacy of Predictions under Service 
Conditions 

The patrol reports of submarines which have used 
the bathythermograph in service contain a number 
of testimonials to the adequacy of its predictions such 
as the following. 

“There was a layer, invariably between 100 and 200 feet out- 
side the 100-fathom curve. In each case the layer necessitated 
much flooding in to get down and pumping out to get back 
up. The bathythermograph predicted the necessary procedure 
nearly every time.” 

“It was found that in changing depth from periscope depth 


to 300 feet through a temperature gradient, the trim was never 
off more than 500 pounds whenever the card indications were 
followed.” 

“We checked the bathythermograph on each deep submer- 
gence for information of the Diving Officer which enabled him 
to adjust his trim so that during search following each attack 
while we were deep he never had to pump, blow or increase 
speed to maintain depth.” 

“Cards graduated to 2,000 pounds per 100 feet were used and 
ballast changes indicated agreed very nearly with those actually 
required. Most dives from periscope depth to 350 feet required 
flooding in about 5,000 pounds.” 

These reports represent selected testimony from sub- 
mariners who have used the BT with understanding 
and perhaps under especially favorable circum- 
stances. In some cases where difficulties have been 
experienced the result can be attributed to the pres- 
ence of salinity gradients, in other cases to the use of 
the wrong isoballast-line grid. Thus one submarine 
reported; 

“The bathythermograph was very helpful in indicating to 
the Diving Officer the presence of density gradients and whether 
they were positive or negative. However, it did not give a true 
indication of the amount necessary to pump or flood.” 

This submarine was found to be using cards designed 
for compressions of 4,000 to 6,000 pounds per 100 
feet although it belonged to a class of 1,400 pounds 
compression. In a group of 49 submarines checked, 
it was found that 64 per cent were using the correct 
card, 20 per cent were using the wrong card, and 16 
per cent were using cards without isoballast lines 
which had been issued before the introduction of this 
feature. 

In order to obtain an overall impression of the 
precision of BT predictions under general service 
conditions, an examination has been made of BT 
records, returned by submarines to the Hydrographic 
Office, on which notations of the actual ballast change 
made in diving are entered. From the record itself 
the predicted ballast change has been estimated and 
compared with that actually made. All cases where 
there was evidence of unreliable trims due to high 
speed or other cause were eliminated and wherever 
tliQ wrong isoballast-line grid was employed the rec- 
ord was transferred to the correct grid before the 
prediction was made. In some cases it is possible that 
the notation on the card was not properly interpreted. 

In the case of 307 dives in which about 45 sub- 
marines participated the predicted ballast change 
agreed with that actually made within the following 
limits: 

18 per cent shifted the predicted amount of ballast 





PRECISION OF BATHYTHERMOGRAPH PREDICTIONS 


33 


49 per cent shifted within 1,000 pounds of the pre- 
dicted amount 

71 per cent shifted within 2,000 pounds of the pre- 
dicted amount 

81 per cent shifte'd within 3,000 pounds of the pre- 
dicted amount 

19 per cent shifted over 3,000 pounds more than 
the predicted amount 

Thus it appears that the chances are about even that 
the prediction will fall within 1,000 pounds of the 
amount actually shifted. The predictions which err 
within this probable error are readily accounted for 
by the several sources of inaccuracy which have been 
discussed. It seems probable that the larger errors are 
in many cases due to poor trims either before or at 
the end of the dive or both. The records of 25 div 
which were excluded from this study because they 
contained evidence that unsatisfactory trims had 
been achieved, chiefly because of high speed, show 
that in 18 cases (76 per cent) the ballast change dif- 
fered from the prediction by more than 3,000 pounds. 
Undoubtedly in many of the dives included in the 
study, bad trims were obtained but were unrecorded. 

A further breakdown of the data shows that of 253 
dives in which the ballast change differed from the 
prediction, more ballast was shifted than the predic- 
tion called for in 130 cases (51.5 per cent) and less in 
123 cases (48.5 per cent). This distribution suggests 
the absence of any preponderant systematic error in 
the predictions. A closer scrutiny shows, however, 
that this result is probably the consequence of two 
opposed tendencies. 

When the observations made during descent are 
separated from those made during ascent it is found 
that in descent less ballast is shifted than called for by 
the prediction in 55 per cent, more in 45 per cent of 
the 157 cases. The tendency to shift less than pre- 
dicted is particularly great in descents made under 
conditions of unstable buoyancy where pumping is 
called for. In 36 such descents less ballast was shifted 
in 61 per cent of the cases; more in only 39. There is 
thus evidence of a conservative tendency on the part 
of diving officers to shift as little ballast as need be, 
thus causing ballast changes to tend to be less than 
the predictions. 

On the other hand, observations made during 
ascent reveal an opposite tendency. In 96 ascents it 
was found that more ballast was shifted than called 
for by the prediction in 63 per cent of the cases, less 


in 37 per cent of the cases. This disproportion was due 
to the dives made under stable buoyancy conditions 
when ballast was pumped out during ascent. In this 
group of 73 cases more ballast was pumped than pre- 
dicted in two-thirds of the ascents. In 23 ascents in 
which ballast was flooded during ascent the amount 
flooded exceeded the prediction in 12 cases and was 
less in 11. The result may be explained by the fact, 
discussed in Chapter 7, that submarines tend to be- 
come heavy during deep submergence, from leakage 
and cooling of the ballast water. Consequently when 
they ascend, additional ballast water must be pumped 
to compensate for this gain in weight. 

6.2.6 Errors Due to Salinity Gradients 

It has been pointed out in Chapter 2 that within 
the depths accessible to submarines, large areas of the 
ocean are free of salinity gradients large enough to 
seriously affect diving operations. In many other re- 
gions, significant salinity gradients are known to 
occur. In order to see how greatly such gradients affect 
BT predictions, two groups of records were selected 
from those returned from submarines in service for 
further study. One group contained 98 cases in which 
the dive occurred in water believed to be free of sig- 
nificant salinity gradients; the second contained 106 
cases in which the presence of salinity gradients could 
be predicted from information contained in the Sub- 
marine Supplements to the Sailing Directions. A com- 
parison of these groups with the entire group is given 
in Table 2. 

Table 2. Comparison of Ballast Changes with Bathy- 
thermograph Predictions. 


Difference between 
ballast change and 
prediction 

Total 

group 

(307 

cases) 

Salinity 
gradients 
absent 
(98 cases) 

Salinity 
gradients 
present 
(106 cases) 

None 

18 

18 

19 

Less than 1,000 lb 

49 

60 

44 

Less than 2,000 lb 

71 

85 

64 

Less than 3,000 lb 

81 

89 

78 

More than 3,000 lb 

19 

11 

22 

Equal to prediction 

18 

18 

19 

More than prediction 

42 

37 

53 

Less than prediction 

40 

45 

28 


Numbers indicate the percentage of cases in each category. 


These statistics indicate that BT predictions are 
much more precise under conditions when salinity 


34 


PREDICTION OF BUOYANCY CHANGES 



Figure 15. Frequency distribution of errors in bathythermograph predictions made by submarines in service. 


A. Based on 98 cases in which errors due to salinity 
gradients were probably absent. 

B. Based on 106 cases in which errors due to salinity 
gradients were prol)al)ly present. 

Ordinate— number of cases which fall in each class interval. 

gradients are believed to be absent. Under such con- 
ditions there is a tendency to shift less ballast than is 
required by the prediction. The presence of salinity 
gradients very definitely decreases the proportion of 
errors which fall within any stated limit. These find- 
ings are brought out more clearly in Figure 15 which 
shows the frequency distribution of errors of different 
magnitude in the two series of data. Dives made in the 
presence of salinity gradients very definitely show an 
increase in the proportion of cases in which more 
ballast is shifted than called for by the prediction 
based on the BT tracing, and also indicate an increase 
in the magnitude of the errors in this direction. 
Salinity errors in BT predictions are likely to arise 


Abscissa— classes of error. Positive values indicate that 
ballast change exceeded prediction, negative that ballast 
change was less than prediction. 

Class intervals are 1,000 lb except for the interval be- 
tween +750 and -750 lb. 

in two sorts of situations. The first of these is in 
coastal waters where the effluence of rivers dilutes the 
surface waters and produces salinity gradients. These 
in turn accentuate the influence on density of the 
strong shallow temperature gradients which develop 
in summer (Figure 8, Chapter 2). The second is at the 
margins of the great currents such as the Gulf Stream 
or the Kuroshio where more dilute coastal water 
tends to overflow the saline oceanic water and pro- 
duces a salinity gradient embedded in a positive tem- 
perature gradient (Figure 11, Chapter 2). 

The following table illustrates the errors inherent 
in using the BT in the former situation. The data 
were obtained during tests with a United States sub- 




PRECISION OF BATHYTHERMOGRAPH PREDICTIONS 


35 




1 TEMPERATURE | ^ 

LlfLh 


1 CONDUCTIVITY SALINITY H A Pj |- 

H buoyancy] 

1 PRESSURE 1 — H CAZ 

1 PRESSURE |— — 

— H DEPTH 1 


Figure 16. Arrangement of components of model CXJC 
buoyancy recorder. 


marine in the Gulf of Maine off Portsmouth, New 
Hampshire, an area where strong shallow tempera- 
ture gradients accompanied by salinity gradients oc- 
cur in the late summer. The buoyancy changes due to 
salinity were estimated from chemical analyses of the 
water at the various depths. 


Table 3. Comparison of Ballast Changes Required to 
Maintain Good Trim and Bathythermograph Predic- 
tions. Off Portsmouth, N. H., September 1943. 


Keel 

depth 

(feet) 

Ballast 

change 

(pounds) 

Bathy- 

thermograph 

prediction 

(pounds) 

Error in 
prediction 
(pounds) 

Buoyancy 
change due 
to salinity 
(pounds) 

64 

0 

0 

0 

0 

77 

7,100 

5,000 

-2,100 

2,600 

100 

8,100 

5,500 

-2,600 

3,070 

200 

8,100 

6,000 

-2,100 

4,100 


Ballast changes in pounds are cumulative from 64 feet. 
Bathythermograph prediction assumes compression of 1,400 
pounds per 100 feet. 


It may be seen that the BT underestimated the ballast 
change by about 30 per cent. The error is rather more 
than accounted for by the measured salinity gradient. 

To meet situations of this sort the following rule 
serves to warn the diving officer of the character of the 
errors produced by salinity gradients if present: 

When the temperature decreases with depth, the 
salinity gradient will occur at the same depth as the 
thermocline. In making ballast adjustments allow 
for greater increase in buoyancy than the BT record 
indicates. 

Whenever cold coastal water overlies the warmer 
water of an ocean current it is certain that a salinity 
gradient is present, since otherwise the water column 
would be unstable and the stratified condition could 
not persist, as explained in Section 2.6. Under these 


circumstances, BT predictions based on the tempera- 
ture gradient are quite misleading. This is illustrated 
by the following measurements made on a United 
States submarine during a dive off the southern coast 
of New England near the inner margin of the Gulf 
Stream. The hydrographic situation observed during 
this dive is illustrated in Figure 11, Chapter 2. 

Table 4. Comparison of Ballast Changes Required to 
Maintain Good Trim and Bathythermograph Predictions 
Off Southern New England Coast April 1943. 


Error Buoy- 
BT in ancy 

Keel Salin- Ballast predic. predic- due to 

depth Temp. ity change tion tion salinity 

(feet) (F) (Yoo) (pounds) (pounds) (pounds) (pounds) 


90 

41.1 

32.99 

0 

0 

0 

0 

150 

41.1 

32.94 

—2,000 

—1,200 

800 

—210 

200 

43.7 

33.40 

—2,000 

—2,200 

—200 

1,720 

250 

49.4 

34.54 

—1,000 

—6,800 

—5,800 

6,510 

275 

51.3 

34.88 

—1,000 

—8,100 

—7,100 

7,940 

312 

52.8 

34.90 

—3,000 

—9,700 

—6,700 

8,020 

90 

42.6 

33.06 

—1,500 

—600 

900 

290 


Ballast changes in pounds are cumulative from 90 feet. 
Bathythermograph prediction assumes compression of 2,000 
pounds per 100 feet. 


It will be noted that although there is a very large 
error in the prediction, this error is rather closely 
accounted for by the measured salinity gradient. The 
salinity gradient coincides closely in depth with the 
temperature gradient, since both arise from the dis- 
continuity of the layers of cold and warm water which 
occurs at the depth of about 200 feet. Actually very 
little ballast change was required, so closely did the 



«#«rr €<500009. 

• c * r e e c © © o 0 o o o ■» » • • • # # <- e c c o o -> 



Figure 17. Measuring unit of model CXJC buoyancy 
recorder. 


iCoMii)K:nT\r j 


36 


PREDICTION OF BUOYANCY CHANGES 


effects of temperature and salinity balance one an- 
other. At the depths where the gradients were strong- 
est, however, the buoyancy actually increased, as 
shown by the fact that 1,000 pounds of ballast was 
pumped between 200 and 250 feet. The submarine 


was balanced at this depth in spite of the strong posi- 
tive temperature gradient. 

Observations of this sort have led to the following 
rule for ballast adjustments in the presence of posi- 
tive temperature gradients: 



Figure, 18. Model CXJC computing mechanism. The tem|)erature bridge is swung out to give access to parts within. 
One amplifier has been removed. 


THE SALINITY CORRECTED BUOYANCY RECORDER 


37 


\\^hen the temperature increases with depth, a 
salinity gradient is always present. It will at least 
counterbalance the influence of temperature on buoy- 
ancy. The isoballast lines cannot be used to predict 
ballast changes. Do not pump more ballast than when 
diving in isothermal water. The salinity gradient 
may be great enough to produce stable buoyancy; in 
this case ballast may need to be flooded on descent 
and balancing will be possible. 

63 the salinity corrected 

BUOYANCY RECORDER 

rhe model CXJC is an instrument which takes 
account of the salinity as well as the temperature of 
the water in which the submarine operates. In order 
to determine the ballast changes necessary to keep the 
\ essel in good trim continuous measurements of tem- 
perature, salinity, and pressure are made. 

The salinity of the water is determined by the 
simultaneous measurement of its temperature with 
the aid of a resistance thermometer and of its electric 
conductance using a conductivity cell. These two 
electrical measurements are combined by means of 
suitable computing mechanisms to yield a voltage 
proportional to the effect of salinity on the density of 
the water. 

The temperature of the water is also converted by 
similar means to yield a voltage proportional to the 
effect of temperature on the density of the water. 

The pressure of the water acting on a Bourdon 
spring controls an arrangement which yields a volt- 
age proportional to the effect of compression with 
depth on the buoyancy of the submarine. 

The three resulting voltages are combined to actu- 
ate a servo motor which moves the writing point of 
the buoyancy recorder horizontally in proportion to 
the change in buoyancy resulting from both the 
change in density of the water and the compression 
effect with change in depth.^ 

The system is shown schematically in Figure 16. 

The CXJC is designed to include a second record- 
ing instrument which through similar mechanisms 
combines the temperature and conductivity measurc- 

The integration of the density function of temperature and 
the density function of salinity depends upon the approxima- 
tion that the density function of temperature is the same at any 
salinity and that a given change in salinity has the same effect 
on density at any temperature. This assumption is not quite cor- 
rect and leads to some error when measurements are made over 
very large ranges in temperature or salinity. 



Figure 19. Model CXJC buoyancy recorder. 


merits to write a graphic record of sound velocity as a 
function of depth. The details of the sonar recorder 
need not concern us, however. 

The measuring unit of the CXJC, which consists of 
a resistance thermometer bulb and a conductivity 
cell, can be mounted either in a line of circulating 
water within the vessel or external to the hull. (See 
Figure 17.) In the former position water is pumped 
through the cell and may be drawn from near the 
level of the center of buoyancy, which is the appro- 
priate position in respect to buoyancy estimations. 
The internal position is advantageous since it per- 
mits ready cleaning to remove fouling growths. The 
external cell may be mounted high on the shears in a 
position favorable for securing information on sonar 
conditions close to the sea’s surface and for obtaining 
advance information on buoyancy conditions during 
ascent. An external cell has also been designed which 
can be mounted at the lower end of a pipe passing 
downward through a main ballast tank so as to 
emerge at the level of the bilge keel. The pipe permits 
the measuring unit to be withdrawn for cleaning 
when the submarine is surfaced. The measuring units 
in the external positions depend on the motion of 
the vessel to force water through the conductivity 
cells. 

The computing mechanisms are assembled for the 


38 


PREDICTION OF BUOYANCY CHANGES 


BOUYANCY CHANGE IN THOUSANDS OF POUNDS OF BALLAST 



Figure 20. Chart used in model CXJC buoyancy recorder 
showing simulated buoyancy trace. Reduced to 1/2 natural 
size. 

most part in a separate case which can be located 
wherever convenient. (See Figure 18.) The recorders 
are kept as compact as possible so as to be suitable for 
mounting on the diving-instrument panel. 

The buoyancy recorder is pictured in Figure 19. 
It carries controls which permit recording to be 
switched from one of two alternate positions of the 
measuring units, i.e., from the shears to the center 
of buoyancy position. An automatic adjustment as- 
sures that the record will always show the condition 
of buoyancy at the depth where the measurement is 
made, irrespective of the position on the hull of the 
measuring unit. 

An adjustment is provided so that the magnitude 
of the influence of compression with depth can be 
varied. 1 he same instrument and card thus can be 
used with vessels of any compression. 

The position of the pen which records the buoy- 
ancy is normally adjusted so that a zero setting may 
be made whenever a good trim is obtained. Subse- 
quent buoyancy changes are thus indicated directly 
and can be used as a guide for ballast changes. This 
arrangement permits an expanded scale of good legi- 
bility to be used over the full range of density to be 
found in fresh or salt waters. 

Figure 20 shows the card used in the buoyancy 
recorder of the CXJC. The record is drawn as it 
would appear for a boat of compression equal to 


2,000 pounds per 100 feet, diving from periscope 
depth in water isothermal to 260 feet below which 
depth a strong density gradient is encountered. The 
part of the record sloping to the right from 50 to 260- 
foot depth indicates the result of compression, the 
sole influence on buoyancy while in water of uniform 
density. At 260 feet the submarine should pump 4,000 
pounds to restore good trim. The record indicates 
that at 300 feet the buoyancy of the submarine would 
be the same as at periscope depth and no ballast ad- 
justment would be required. To be in trim at 400 
feet, the submarine should flood 12,000 pounds. This 
record is very much easier to interpret than that of 
the earlier types of bathythermograph. An experi- 
mental CXJC has been given preliminary tests. The 
results indicate that it will predict ballast changes as 
accurately as the submarine can be trimmed and its 
compression adjustment can be set. Table 5 shows the 


Table 5. Comparison of Buoyancy Changes Recorded by 
CXJC and Those Calculated from Measurements of Tem- 
perature and Salinity. 


Temperature 

F 

; Salinity 

“/oo 

Buoyancy change 
pounds 

Calculated 

Recorded 

Dillerence 

35.5 

31.51 

0 

0 

0 

36.2 

30.88 

2.700 

2,600 

-MOO 

36.9 

30.61 

4,320 

4,200 

+ 120 

38.1 

29.23 

9,720 

10,200 

-480 

38.4 

26.24 

23,220 

22,800 

+ 420 

40.6 

22.65 

38,870 

38,600 

+ 270 


precision with which the buoyancy indications fol- 
lowed that of the sea water during a surface run 
through waters varying greatly in salinity. 

Table 6 shows a comparison of ballast changes and 
buoyancy predictions during several experimental 
test dives in water in which strong salinity gradients 
were present. 

Table 6. Comparison of Ballast Changes with Predictions 

of CXJC. 

Depth — feet Ballast change — pounds 


CXJC Actual 


From 

To 

prediction 

change 

Difference 

60 

400 

+ 6,000 

+ 5,000 

1,000 

400 

200 

0 

0 

0 

200 

100 

-2.000 

-2,000 

0 

60 

400 

+ 2,000 

+ 2,500 

500 

400 

100 

-1,000 

-1,300 

300 


Chapter 7 

CHANGES IN BUOYANCY DURING PROLONGED 
SUBMERGENCE 


S ubmarines tend to become heavy during submerg- 
ence. The effect is referred to as “soaking up” and 
is attributed to losses of air from the interstices of 
pervious structures such as woodwork and rope or 
cable and from the multiplicity of crevices in which it 
might be entrapped. How great the effect of such 
entrapped air may be is unknown. There are, how- 
ever, at least three other sources of lost buoyancy 
during submergence: (1) the permanent set of the 
hull due to compression, (2) leakage, and (3) cooling 
of the hull, ballast water, and fuel oil. 

The prevalence and magnitude of the soaking-up 
effect is indicated by records of ballast changes made 
by submarines in service. In a group of 68 dives made 
by 13 different vessels in which the ballast change on 
both descent and ascent was reported, more ballast 
was pumped than was flooded in 49 cases; in only 7 
dives, more was flooded than was pumped. In 12 
dives nearly the same amount was shifted in descent 
and ascent, but this included 8 cases in which no 


22 







_ 

20 





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- 

18 





1' ' 


_ 

1 1 1 ' o 








(f) 








O 14 







- 

U- 

O 12 

OC 

m 10 

- 


I 

P 

% 

"I 


- 

i 8 

6 

: 



y i 




_ 

4 





-4f- 



_ 






/f’ 




2 





^ / 

4 ' 





r 1 










4 3 

1 

2 

r 

1 

r 

0 

1 

-2 

1 

-3 

1 

-4 

T T 

-5 -6 


BALLAST FLOODED MINUS BALLAST PUMPED 
THOUSANDS OF POUNDS 

Figurk 1. Frequency distribution of difference between 
ballast change on descent and on subsequent ascent by 
submarines in service. Ordinate— number of cases; ab- 
scissa-class intervals of 1,000 lb difference. 


ballast was shifted. Figure 1 shows the frequency with 
which the ballast flooded differed from that pumped 
by various amounts. It shows that commonly the 
soaking-up effect amounts to about 2,000 pounds and 
that occasionally much larger effects are experienced. 

These reported dives were made for the most part 
in water in which considerable negative temperature 
gradients were encountered and the result may be 
due in part to a gain in weight resulting from the 
cooling of the ballast water. However, in the dives 
made in the absence of such gradients, the same dis- 
crepancy between the amount of ballast Hooded and 
pumped existed which cannot be accounted for in 
that way. 

Information on the prevalence of lost buoyancy 
during submergence is given also by the results of 
compression tests in which the apparent compression 
on descent is compared with the value obtained on 
ascent. If the submarine is becoming heavier from 
any cause during descent, more ballast will need to be 
pumped to obtain good trim at the greater depth 
than is required by the true compression and by the 
density gradients which may be present. Conse- 
quently, the compression estimate will be too high. 
On ascent, on the other hand, less ballast will be 
flooded and the compression estimate will be too low. 
The difference between the compression estimates on 
descent and ascent consequently gives a measure of 
the change in buoyancy during the dive. 

Analysis has been made of 53 dives, made in the 
course of deep submergence tests on new construc- 
tion submarines, in which compression was estimated 
both on descent and ascent. The difference between 
the estimates is presented as a histogram in Figure 2 
which shows the number of dives in which the com- 
pression on descent exceeded that on ascent by vari- 
ous amounts. The mean difference is 1,200 pounds, 
the median difference 1,000 pounds, and the modal 
difference 600 pounds per 100 feet. When the data 
are separated into “good” and “poor” tests on the 
basis of the observers’ judgment, it appears that the 
poor tests account for many of the large differences. 
This is explained by the fact that poor tests fre- 


J)M il)i:N I 1 At. / 


39 


40 


CHANGES IN BUOYANCY DURING PROLONGED SUBMERGENCE 


quently arise from hasty trims on the return to peri- 
scope depth and that tests are judged poor if leakage 
is excessive. The good tests, however, show that the 
compression estimate is usually larger on descent 
than on ascent. 

Further analysis of this data has failed to show any 
clear indication that the differences in compression 
estimates are related to the duration of submergence 
although this is to be expected. There is some slight 
suggestion that greater differences are obtained if 
dives are made into negative temjDerature gradients 
than in isothermal water or into positive gradients as 
is to be expected if cooling leads to a loss of buoyancy. 

The results of this study are summarized in Table 1 . 


Table 1. Difference in Compression on Descent and Ascent, 
(pounds per 100 feet) 



Number 
of tests 

Mean 

Median 

Mode 

All tests 

53 

L200 

1,000 

600 

All GOOD tests 

30 

800 

500 

500 

All POOR tests 

13 

1,900 

1,700 

* 

Duration of dive 

All tests 

Less than 2 hours 

20 

1,000 

1,000 

1,000 

More than 2 hours 

24 

1 ,300 

1,000 

* 

GOOD tests 

Less than 2 hours 

11 

700 

500 

* 

More than 2 hours 

14 

800 

500 

* 

l emperature gradient 

All tests 

Negative 

23 

1 ,400 

1 ,200 

700 

Isothermal or positive 

27 

1 ,000 

800 

200 

(;OOD tests 

Negative 

11 

1 ,000 

* 

* 

Isothermal or positive 

18 

600 

500 

* 


* Indeterminate. 


7 1 PERMANENT SET OF HULL DUE 
TO COMPRESSION 

Batten measurements have been made on subma- 
rines during the initial deep-submergence tests con- 
ducted in Lake Michigan off Manitowoc, Wisconsin. 
These measurements have shown that there is a per- 
manent set of the pressure hull, when a submarine 
first submerges to the test depth, which decreases its 
diameter 0.01 inch on the average. This corresponds 
to a difference in buoyancy of approximately 200 
pounds per 100 feet. The compression tests listed 
above were conducted on submarines during the ini- 



o 



DIFFERENCE IN COMPRESSION 


Figure 2. Frecpiency distribution of differences between 
compression estimates made on descent and ascent. The 
differences represent compression on descent minus com- 
pression on ascent. The difference in compression is 
shown in units of 100 lb; the class intervals correspond- 
ing to 600 lb. 

tial deep submergence, although some boats had sub- 
merged previously to 200 or 300 feet and almost all 
had been to a depth of at least 100 feet. The range in 
depth during the compression tests averages about 
300 feet. The permanent set of the pressure hull, 
therefore, can be expected to account for as much as 
200 pounds of the difference in compression during 
the descent and ascent noted above. This effect ac- 
counts for only a small part of the difference noted 
in the “good tests” of new submarines being tested 
for compression. It seems unlikely that it is an im- 
portant factor in the soaking up of submarines in 
service which previously have made repeated dives to 
considerable depths. 

72 LEAKAGE 

Sid^marines almost always leak somewhat. New 
vessels undergoing preliminary trials frequently leak 
severely as may those which have been damaged dur- 
ing service. The rate of leaking increases with depth 
and may be 10 or 12 times as great during deep sub- 


ftxjM IDK.N^ I \-tr-A 


COOLING OF HULL, BALLAST WATER, AND FUEL OIL 


41 


mergence as at periscope depth. While it is impossible 
to make any quantitative generalizations in regard to 
rate of leakage, since this depends on the condition of 
the particular vessels, it is probable that leakage is 
often the principal factor causing submarines to be- 
come heavy during submergence. 

7 3 COOLING OF HULL, BALLAST WATER, 
AND FUEL OIL 

When a submarine descends into a temperature 
gradient, cooling of the hull, ballast water, and fuel 
oil may be expected to produce a loss in buoyancy. As 
a result, ballast may need to be pumped from time to 
time during a prolonged stay at deep submergence to 
retain good trim. If this compensation is not made, 
the ballast change required on returning to periscope 
depth will differ from that made in descent, and more 
ballast must be pumped out, or less flooded in, to 
regain good trim. After returning to the layers of 
warm water near the surface, a submarine which has 
cooled off during deep submergence will become 
lighter as it warms up and subsequent adjustments of 
trim may be required. 

In order to estimate the magnitude of these effects, 
it is convenient to divide the displacement of the sub- 
marine into three parts, each displacing about 1.8 x 
lO^’’ pounds. 

1. The displacement of the ends of the vessel which 
are exposed directly to the temperature of the sea 
water. 

2. The displacement of the midpart of the pres- 
sure hull which is protected from the temperature of 
the sea by the main ballast and fuel tanks. 

3. The displacement of the main ballast and fuel 
tanks. 

The coefficient of linear thermal expansion of steel 
is 5.84 X 10“^‘ per degree F; consequently, the coeffi- 
cient of cubic expansion of a steel structure will be 
17.5 X 10 per degree F. 

Consider first the immediate effect of entering 
water of lower temperature. It may be assumed that 
the exposed steel will at once acquire the temperature 
of the water but the temperature of the ballast water 
and fuel oil will remain unchanged. The contraction 
of the ends of the submarine will result in a decrease 
in buoyancy of 17.5 x lO"^* x 1.8 x 10^* or 31.5 pounds 
per degree F. The displacement of the pressure hull 
within the ballast tanks will remain unchanged. The 
contraction of the walls of the ballast tanks will cause 


some change in their displacement, but this will be 
almost exactly balanced by a loss in weight which re- 
sults from the escape of an equal volume of water 
from the openings in the bottom of the tanks and the 
vents. Consequently, only the contraction of the ends 
of the submarine will contribute to the immediate 
loss in buoyancy and this will amount to only 31.5 
pounds per degree F. This effect will not be detect- 
able unless the temperature change exceeds 16 F and 
will never become important. 

If the submarine remains in the water of lower 
temperature, the ballast water and fuel oil will be- 
come colder and more dense as the result of heat 
transfer through the walls of the tanks and because 
of an exchange of water between ballast tanks and 
sea by way of the available openings as the result of 
convection. When these processes have come to an 
end and the submarine is in thermal equilibrium 
with the sea water, the buoyancy will have decreased 
still further. 

As the result of cooling the walls of the mid-section 
of the pressure hull within the ballast tanks, the dis- 



100 200 300 400 500 600 


CHANGE IN BUOYANCY IN POUNDS /°F 

Figure 3. Relation between quantity of fuel oil carried 
and the change in buoyancy, as a result of cooling, of a 
submarine of 2,400 tons submerged displacement. Com- 
plete thermal equilibrium between the sea water and the 
contents of the ballast tanks is assumed. 


42 


CHANGES IN BUOYANCY DURING PROLONGED SUBMERGENCE 


placement will decrease 17.5 x 1(H x 1.8 x 10® or 31.5 
pounds per degree F. 

.\s a result of the cooling of the ballast water and 
fuel oil, the weight of the vessel will increase and the 
net buoyancy will be decreased accordingly. The 
change in density of the water per degree depends 
upon the temperature as indicated in Section 4.5. At 
60 F it amounts to 0.000124 per degree F. Conse- 
quently, if the fuel oil tanks as well as the main bal- 
last tanks were filled with sea water, the net buoy- 
ancy would decrease 0.000124 x 1.8 x 10® or 223 
pounds for each degree decrease in temperature. 

The change in net buoyancy when a submarine 
attains thermal equilibrium at a temperature 1 F 
lower than that previously obtaining, assuming that 
all external tanks are filled with water, is summarized 
in Table 2. 


Table 2. Change in Net Buoyano of a Submarine of 
2,400 Tons. Submerged Displacement Due to a Tem- 
perature Change of 1 F. 


Temperature F 

40 

60 

80 

h 

Q. 

< 

1 

0.000060 

0.000124 

0.000175 

Decrease in Buoyancs 
(pounds per F) 

Immediate cooling of ends 

31.5 

31.5 

31.5 

Final cooling of mid-section 

31.5 

31.5 

31.5 

Final cooling of 800 tons of 

ballast water 

108.0 

223.0 

315.0 

Total 

171.0 

286.0 

377.0 


The change in net buoyancy due to cooling of fuel 
oil is greater than that due to cooling of an equivalent 
amount of ballast water. The average change in den- 
sity per degree for fuel oil of the specific gravity used 
is —0.0004, considerably more than for water. The 
maximum capacity of the Normal Compensating 
Fuel Oil Tanks of a representative fleet-typ)e subma- 
rine is approximately 195 tons of fuel oil. The maxi- 
mum total fuel oil capacity is approximately 350 tons 
of fuel oil. Figure 3 shows the total change in buoy- 
ancy f)er degree due to all causes for a submarine 
with 2,400 tons displacement and having different 
amounts of fuel oil aboard, from 0 to 400 tons. This 
graph assumes that thermal equilibrium has been 
attained, a condition which rarely exists. 

It is evident from Figure 3 that substantial trim 
adjustments will be required to compensate for the 
effects of cooling if a submarine dives into water 
more than 4 or 5 degrees F colder than that from 


which it is in equilibrium at the start. The more fuel 
oil aboard, the more pronounced will be the loss ol 
buoyancy due to cooling. The effects will be particu- 
larly pronounced if the water and fuel oil in the tanks 
is warm, i.e., when operating in the tropics or in late 
summer. 

The influence of the various effects of cooling on 
the buoyancy of a submerged submarine is illustrated 
in Figure 4. Curve A illustrates the way in which 
buoyancy changes as the result of the effect of tem- 
perature on the density of the displaced water, assum- 
ing no change in the displacement of the submarine. 
Curve B is corrected to include the immediate change 
in buoyancy due to the contraction of the ends of the 
hull which are not protected by the ballast tanks.® 
Curve C shows the relative buoyancy of the subma- 
rine with all main ballast and fuel oil tanks filled 
with water and assuming this ballast water to be in 
thermal equilibrium with the sea at each tempera- 
ture. Curves D, E, F, and G show relative buoyancy 
in thermal equilibrium with various amounts of fuel 
oil aboard. 

The change in buoyancy arising from the cooling 
of the contents of the ballast tanks is related to the 
change in buoyancy which the vessel experiences 
when it first changes depth, since both depend on the 
change in temperature encountered. Roughly speak- 
ing, since the ballast tanks account for one-third the 
total displacement, one-third of the increase in buoy- 
ancy encountered on diving into colder water will be 
lost as the contents of the tanks cool. Consequently, 
about one-third of the ballast flooded in during a 
descent may need to be pumped out again as the 
cooling takes place. 

AVhile this may serve as a useful working rule in 
anticipating the effects of cooling during prolonged 
submergence, it is not very precise. More exactly, the 
quantity of fuel oil present in the ballast tanks and 
the effect of compression on buoyancy must also be 
taken into account. The fundamental relations are as 
follows: 

Let: AWf = change in weight due to cooling of bal- 
last tank contents. 

R = fraction of displacement, T, occupied 
by ballast tanks. 

a Since this effect is small, it has not been taken into account 
in buoyano calculations or in the design of bathythermographs. 
With improvements in the art of trimming submarines, it may 
l>ecome desirable to do so. 


RELATIVE BUOYANCY IN POUNDS 


COOLING OF HULL, BALLAST WATER, AND FUEL OIL 


43 


40,000 


35,000 


30,000 


25,000 


20,000 


1 5,000 


10,000 


5,000 


30 40 50 60 70 80 90 

TEMPERATURE OF WATER 

Figure 4. Effect of temperature on the buoyancy of a submarine of 2,400 tons submerged displacement: 

A. Assuming no change in displacement of hull due to cooling, 
li. Allowing for immediate cooling of steel of ends of bull. 

C. Allowing for thermal equilibrium between sea water and content of ballast tanks and assuming 800 tons dis- 
placed by ballast tanks to be occupied by sea water. 

D. Same but assuming 100 tons of fuel oil to be present in ballast tanks. 

E. Same but assuming presence of 200 tons of fuel oil. 

F. Same but assuming presence of 300 tons of fuel oil. 

G. Same but assuming presence of 400 tons of fuel oil. 

fixiXl 11)L\ 1 I 



44 


CHANGES IN BUOYANCY DURING PROLONGED SUBMERGENCE 


r = fraction of displacement, V, occupied 
by fuel oil ballast. 

R — r = fraction of displacement, V, occupied 
by sea water ballast. 

Apt = change in density of sea water due to 
cooling. 

Ap't = change in density of fuel oil due to 
cooling. 

Then: 

{R-r)V Apt — change in weight due to cooling of sea 
water ballast. 

rVApt — change in weight due to cooling of fuel 
oil ballast. 

Therefore: 

ATT, = {R - r) VApt + rVApt. (1) 

If A" equals average ratio of Apt to Apt over the tem- 
perature range in question then: 

Apt = KApt. 

Equation (1) may then be written: 

AWt= [R + (A-l)r] VAp,. (2) 

In order to compare the change in weight due to 
cooling with the change in ballast, ATT, required to 
adjust buoyancy at the time of the dive, we may write 
equation (5), Section 3.3 as: 

ATT = VApt + CaZ, (3) 

substituting Apt for Apts since salinity effects must be 
left out of account. Combining equations (2) and (3): 

ATT^, = [R + (A-l)r] (ATT - CaZ). (4) 

In order to see the numerical meaning of equation 
(4) we may take R = 1/3. Depending on the amount 
of fuel oil carried, r = 0 to 1 /6. A = about 4 at a 
temperature of 60 F. Consequently, if the ballast 
tanks are completely filled with sea water the increase 
in weight due to cooling will equal one-third the bal- 



Ficure 5. Temperature of ballast water in safety tanks, 
with vents open and closed, during deep sidjinergence in 
a negative temperature gradient and after return to peri- 
scope depth. 

last flooded during descent plus one-third the gain in 
weight due to compression. If the fuel tanks contain 
the maximum amount of fuel oil then R -f (A— l)r 
ecjuals 5/6. The increase in weight due to cooling will 
equal 5/6 the ballast flooded during descent plus 5/6 
the gain in weight due to compression. It may be seen 
from this that without taking the quantity of fuel oil 
into account, an exact allowance for the gain in 
weight due to cooling cannot be made. 

The importance of cooling ballast water and fuel 
oil will be discussed further in connection with stable 
buoyancy in the following chapter. 

The rate of cooling or warming of ballast water 
which occurs when a submarine is exposed to a differ- 
ent temperature depends on whether the vents of the 
ballast tanks are closed or open, and probably also on 
whether the ballast water is colder or warmer than 
the surrouhding sea water. If the vents are closed, 
heat transfer is limited by the rate of conduction 
through the steel wall of the ballast tank and by the 
rate of mixing of the water within the tank. If the 
vents are open during descent, convection causes the 
ballast water to escape from the tanks through the 
vents to be replaced by sea water at the temperature 
of that surrounding the hull. On ascending into 
warmer water, colder ballast water can escape 
through the larger openings in the bottom of the 
tanks as the result of convection even though the 


COOLING OF HULL, BALLAST WATER, AND FUEL OIL 


45 


vents are closed.'^ The rate of cooling of the fuel oil 
is limited by conduction through the wall of the tank 
and by the rate of mixing of the fuel oil within the 
tank. 

1 he results of an experiment to test the rate of 
change of the temperature of the ballast water are 
illustrated in Figure 5. The tests were conducted with 
a United States submarine in the Gulf of Panama in 
March 1943 when a temperature gradient of about 
12 F was present. On submerging, the submarine 
filled the ballast tanks with water of 72.5 F and after 
coming to trim briefly at 53 and 120 feet finally lev- 
eled off at 220 feet depth where she remained for 1 
hour. During this dive the temperature of water 
drawn from the inboard vents of the safety tanks was 
measured, as well as that of the surrounding sea 
water, draw'ii from a pressure line in the forward tor- 
pedo room. The outboard vent of the starboard 
safety tank was kept shut during the test, that of the 
port tank was left open. 

The results show that in the tank with the out- 
board vent closed the temperature of the water 
changed very slowly. The rate is only 1.5 F per hour 
during the period when the temperature difference 
is 10 F. In the tank with the outboard vent open the 
temperature change is very much more rapid. The 
temperature difference has been reduced by 80 per 
cent after 55 minutes in the colder water at 220 feet 
keel depth. On returning to the warmer water near 
the surface the tank with open vent warmed much 
more rapidly than it cooled during descent. 

The difference in the rate of temperature change 
in the tank with open vent on descent and ascent is 
explained by the position from which the samples of 
water were drawn. The inboard vents are located at 
the top of the ballast tanks. On descent the warmer 
wafer of the tank escapes from the outboard vent and 
it is not until the colder water, entering at the bottom 
reaches the top, that its effects are felt. On ascent, on 
the other hand, warm water flows into the tank 
through the outboard vent under convective forces 

h It must be assumed that if a submarine descended into a 
density gradient due to salinity, convective forces would pro- 
duce changes in the weight of the ballast water if the vents are 
open, but no information is available on this situation. 


and at once reaches the point at which the samples 
are drawn. 

This consideration indicates that the method em- 
ployed is not very satisfactory. More useful results 
could be obtained by holding the submarine at con- 
stant depth below a thermal gradient and carefully 
determining the ballast adjustments required to 
maintain stop trim at that depth from time to time, 
or by observing the rate at which a submarine sinks 
while balanced in a thermocline, under conditions 
such that the buoyancy of the surrounding water can 
be adequately measured. 

These experiments show quite satisfactorily, how- 
ever, that the rate of cooling of the ballast water is 
very slow if the vents are kept closed and that a sub- 
marine may become markedly heavy within less than 
an hour if the vents are open. Consequently, when- 
ever it is necessary to remain at depth for some time 
without operating the trim ballast pump, the vents 
should be closed unless other considerations require 
that they be left open. 

Four observations on the loss of buoyancy due to 
cooling have been made on fleet-type submarines 
operating in the Key West area and are recorded in 
Table 3. The submarines remained submerged at 


Table 3. Loss of Buoyancy Due to Cooling During Deep 
Submergence. 


Duration of 
submergence 

Surface 

temp. 

Temperature 
decrease 
at depth of 
submergence 

Ballast 

change 

(pounds) 

Decrease 

in 

buoyancy 
(lb per F) 

5 hrs. 30 min. 

71° 

4° 

-4,100 

1 ,033 

3 hrs. 30 min. 

68° 

8° 

-3,400 

425 

5 hrs. 10 min. 

64° 

7° 

-5,800 

830 

No record 

74° 

6° 

-4,500 

750 


some depth for several hours during which the bal- 
last change required to main trim was recorded. If 
these results are compared with the values in Figure 
3, it will be seen that the change in buoyancy per 
degree is greater than that predicted from Figure 3. 
The difference is probably due to leakage. There is 
no information on the amount of fuel oil aboard dur- 
ing any of these tests. 


:()\FinF\ I lAL 


Chapter 8 

STABLE BUOYANCY 


I F THE density of the sea water is very nearly uni- 
form a submarine will become heavier as it de- 
scends or lighter as it ascends because of the effect of 
compression. Any small deviation from the depth at 
which net buoyancy is zero will produce changes in 
buoyancy which cause the vessel to move in a direc- 
tion which leads to still greater changes in buoyancy. 
Consequently, no matter how carefully trim is ad- 
justed to secure neutral buoyancy, constant attention 
is required to hold the submarine at the desired 
depth with the use of the diving planes. Under these 
conditions buoyancy is unstable. 

In contrast, if the density of the sea water increases 
with depth sufficiently, the influence of compression 
on buoyancy is outweighed by the density gradient 
and the submarine becomes lighter as it descends and 
heavier as it ascends. Any small deviation from the 
depth at which net buoyancy is zero will produce 
changes in buoyancy which cause the vessel to return 
to its original depth. Consequently, the submarine 
will hold automatically the depth for which it is 
trimmed. If the vessel is not exactly in trim, it will 
tend to seek the level at which net buoyancy is zero. 
Under these conditions buoyancy is stable. 

It is a great advantage to be able to recognize the 
depths at which buoyancy is stable, since by seeking 
these depths the submarine can be controlled with 
greater ease. 1 he submarine may be actually brought 
to a stop and allowed to float in the density layer 
without use of the planes to control its depth; this 
operation is known as balancing. 

1 wo conditions of stable buoyancy may be dis- 
tinguished. llie first we may call immediate stability. 
It refers to a submarine which has been brought to its 
depth from a region of different temperature and as 
a result is not in thermal equilibrium with the sur- 
rounding water. Such a vessel will tend to hold its 
level for a time, but as the ballast water changes its 
temperature, its weight changes and the submarine 
will tend to sink or rise slowly depending on whether 
the ballast water is cooling or becoming warmer. The 
condition is not strictly a stable one and might better 
be described as pseudo-stability. 

The second condition of stable buoyancy obtains 
after the submarine has come into complete thermal 


DEGREES FAHRENHEIT 



30 40 50 60 70 80 90 


Fir.iiRE 1. Tenipeiatuie trace illustrating condition when 
immediate stability exists between depths A and B. 


equilibrium with the surrounding water. We will 
call this permanent stability, since the vessel will now 
hold its position in a sufficient density layer indefi- 
nitely. 

8 1 IMMEDIATE STABILITY 

The conditions for stability are fulfilled whenever 
AB/AZ has a positive value. If a submarine is in good 
trim at some depth, Z, and no change in ballast is 
made and time is not permitted for the ballast water 
change temperature, it follows from equation (4), 
Section 3.2 that the change in buoyancy on chang- 
ing depth is given by: 

AB/AZ = VApt/AZ + C. 

Remembering that C is a negative number, it is evi- 
dent that the conditions for immediate stability are 
fulfilled when: 


VApf/AZy - C. 

Since VApt/Z is represented by the slope of the 
temperature trace on the bathythermograph card and 
— C is represented by the slope of the isoballast lines, 
it follows that at any point where the temperature 
trace is inclined from the vertical more than the iso- 
ballast lines passing through the tracing at that point, 
immediate stability exists. (See Figure 1.) 

By reference to Section 3.3, it may be seen that the 


PERMANENT STABILITY 


47 


T2 Ti 



Figure 2. Diagram illustrating the change in depth of a 
submarine which when in trim at A descends and bal- 
ances at B and subsequently becomes heavier as the result 
of cooling. 

condition for immediate stability corresponds to that 
in which ballast must be flooded as the submarine 
descends. Consequently, wherever a submarine finds 
that ballast must be flooded in order to descend in 
trim it is passing through a region of stable buoyancy. 

82 PERMANENT STABILITY 

In order to define the conditions for permanent 
stability, consider a submarine changing depth so 
slowly that the ballast water is at all times in thermal 
equilibrium with the surrounding water. If the fuel 
oil ballast tanks were filled with sea water, the buoy- 
ant force due to the displacement would be due solely 
to the displacement of the pressure hull, since the 
weight of the ballast water is at all times equal to the 
weight of the water displaced by the main ballast 
tanks. The small changes in buoyancy resulting from 
the thermal contraction of the steel hull may be 
disregarded. 

If R equals the fraction of the submerged displace- 
ment, V, occupied by the ballast water, then the 
change in buoyancy resulting from any change in 
depth, aZ, is given by (1 —R)V AptI AZ and AB j AZ = 
(l—R) V Apt I AZ-\- C. Conditions of stable buoyancy 
are now fulfilled wherever: 

VApt/AZ > -C/(l - R). 

Since R equals about 1/3, stability obtains when 


T2 T, 



Figure 3. Diagram illustrating condition when perma- 
nent stability does not exist. 


VptAZ is greater than — 1.5 C. This means that 
wherever the temperature trace is inclined to the ver- 
tical more than 1.5 times the inclination of the iso- 
ballast lines, buoyancy is permanently stable. 

It is possible to draw lines on the bathythermo- 
graph chart which define by their slope the condi- 
tions of permanent stability in the same way that the 
ordinary isoballast lines define the conditions of im- 
mediate stability. They may be called lines of perma- 
nent stability. They represent conditions of equi- 
librium in respect to both temperature and buoyancy. 
Their inclination is 1.5 that of the isoballast lines. 
Such lines have found no use in practice as yet but 
they are helpful in considering buoyancy problems. 

Example: In Figure 2, suppose a submarine in trim 
at point A where its ballast water is at the tempera- 
ture Tj descends without changing ballast. On reach- 
ing the depth of point B it will again be in trim, since 
at that depth the loss in buoyancy due to compression 
CaZ equals the gain in buoyancy V Apt resulting 
from the thermal gradient. Since the temperature 
trace is inclined to the vertical more than the isobal- 
last line, immediate stability exists and the submarine 
may balance at B. In this position, however, the sub- 
marine is surrounded by water of temperature T 2 
which is colder than the ballast water. The cooling 
of the latter will cause a small increase in weight AW 
and the submarine will sink through the depth AZ 
until it is again in balance. This process will be re- 


OTO^nrEXTiAT: 


48 


STABLE BUOYANCY 


peated and the point representing the condition of 
the vessel will move downward along the tempera- 
ture trace until C is arrived at; there the ballast water 
will be in thermal equilibrium with the sea and no 
further changes in weight will result from cooling 
and the submarine may balance indefinitely at the 
depth of point C. 

By this graphic procedure an idea can be obtained 
as to how deeply a balanced submarine will settle as 
it cools and whether there is likelihood that it will 
“fall through” a given density gradient. Thus, it may 
be seen from Figure 3 that if the temperature trace 
does not cross the line of permanent stability which 
originates at the point at which the submarine was 
originally in thermal equilibrium, A, then the sub- 
marine will never come into thermal equilibrium but 
will settle until it reaches the point C below which 
even temporary stability does not obtain. 

From consideration of these examples it is evident 
that the following rough rule indicates when a bal- 
anced submarine is in danger of ultimately sinking 
through a density layer as the result of cooling. 

If at the depth of a balanced submarine, or at some 
greater depth, the temperature trace is not inclined 
to the vertical 1 1/2 times more than the isoballast lines 
which cross it, then permanent stability will never be 
reached and the submarine will ultimately sink below 
the density gradient. 

Unfortunately, the high coefficient of thermal ex- 
pansion of fuel oil, and the variable quantity of oil 
which is carried from time to time limits very greatly 
the utility of this rule. Fuel oil will increase in den- 
sity on cooling much more than the sea water which 
it displaces, particularly at low temperatures at which 
the thermal expansion of sea water is relatively small. 
Consequently if much fuel oil is present and if the 
temperature of the sea water is low, much stronger 
temperature gradients must be present to ensure per- 
manent stability than are indicated by the foregoing 
discussion. Indeed permanent stable buoyancy may 
be an impossibility. Reference to Figure 4, Chapter 
7, shows that at low temperatures, submarines carry- 
ing 200 tons of fuel oil or more actually lose buoy- 
ancy as the temperature of the water with which they 
are in equilibrium decreases. Under such conditions 
AB/AZ would have negative value in a negative 
temperature gradient and buoyancy would be un- 
stable. However, since the rate of cooling of the fuel 
oil must be very slow, as judged by the rate of cooling 
of ballast water when the vents are closed, these 


effects of fuel oil on stable buoyancy will not become 
important unless balancing is continued for a long 
time. 

Up to the present time no precise information is 
available on the rate and degree to which submarines 
actually sink when balanced in temperature grad- 
ients, though the fact that they become heavier while 
submerged is well established. The foregoing con- 
siderations are entirely theoretical and have been in- 
troduced into submarine doctrine only to the extent 
of a warning that balanced submarines are liable to 
settle through the thermocline as the result of cooling 
and that density gradients of less than 3,000 pounds 
per 100 feet are unreliable for balancing. It is, of 
course, pointed out that danger of falling through is 
least if balancing is attempted near the upper limit 
of the temperature gradient, and if the main ballast 
tank vents are kept closed during the operation. 

83 BALANCING 

In the past the operation of balancing has been re- 
garded as a stunt, so unreliable that the practice has 
been officially discouraged. This prejudice arose from 
the fact that no means were available to indicate 
whether the submarine could expect to balance or 
not, and submarines were balanced only accidentally 
when their movements were checked by encountering 
heavy density layers or when they happened to come 
to trim in a region of stable buoyancy. It also hap- 
pened sometimes that submarines attempting to bal- 
ance without adequate knowledge of the density con- 
ditions would unexpectedly begin to sink, and as a 
result fear was always present that the vessel would 
fall through the density layer and get out of control. 

The bathythermograph has provided a reliable 
means of predicting whether balancing is possible, at 
what depths it is feasible, and what margins of safety 
exist when balanced at any depth. Since its introduc- 
tion, scores of submarines have recorded the opera- 
tion in their patrol reports, occasionally under con- 
ditions in which it was of great value. In one case a 
submarine reports balancing for as long as 17 hours. 
The uses of the maneuver will be discussed in Chap- 
ter 10. Here it is sufficient to report that conditions 
where balancing is possible are much more frequent 
than was formerly realized and that the strength of 
the requisite gradients appears to be smaller than was 
anticipated. 

While the possibility of balancing depends upon 


THE RATE OF SINKING IN UNSTABLE BUOYANCY 


49 


the rate at which the density of the water increases 
with depth, FApfs/AZ, and the security depends on 
the extent of the gradient below the vessel, as dis- 
cussed above, the ease of bringing the submarine into 
balance at any particular depth depends on other fac- 
tors. To balance at all in the density gradient, the sub- 
marine must be brought into stop trim for some 
depth at which buoyancy is stable, that is between the 
points A and B in Figure 1. The greater the change 
in buoyancy within the limits of stable buoyancy, the 
more easily will the submarine be trimmed correctly 
for balancing. Actually, submarines have been bal- 
anced in gradients in which the buoyancy was stable 
through only a range of 500 pounds. Since this is close 
to the limit of accuracy of trim adjustments, success 
depended somewhat on luck. It should, however, be 
quite easy to bring a submarine to balance in a grad- 
ient of 2,000 or 3,000 pounds range of stable buoy- 
ancy. 

Where operation at a particular depth is at issue, 
the greater the buoyancy change per unit depth, the 
more easily is depth held since large changes in 
weight cause only small changes in depth On the 
other hand, a submarine balanced in a sharp density 
gradient is in greater danger of falling through than 
in one extending over greater depth, since in the 
former case it is given less warning by change in depth 
that its buoyancy is decreasing. 

84 the rate of sinking in 

UNSTABLE BUOYANCY 

Much of the prejudice against balancing which 
previously existed arose from the belief that on sink- 
ing below the density gradient, a submarine would 
become heavy so rapidly that it was in danger of get- 
ting out of control. This was based in part on the 
known effect of compression in decreasing the buoy- 
ancy of a submarine as it went deeper. It was also 
based on the erroneous belief that the buoyancy of 
the water decreased below the “density layer.” In 
order to test this hazard, experiments were made in 
which a balanced submarine was deliberately caused 
to sink through the density gradient by flooding in 
successive small quantities of ballast until it was no 
longer in stable buoyancy. When 500 or 1,000 pounds 
of ballast were flooded in while the submarine was 
balanced near the lower limit of the thermocline, it 
sank at a rate of about 2 feet per minute. When it 
reached the unstable water below the thermocline. 


its rate of fall increased rapidly, as recorded in 
Table 1. 

Table 1. Rate of Sinking of Submarine When out of Trim. 


Amount heavy 

Rate of fall 

pounds 

feet/minute 

500 

3.3 

1,000 

6.6 

3,100 

30.0 

12.000 

50.0 


Unless grossly out of trim, the submarine could 
easily be brought back into balance at the proper 
depth. Even when 3,100 pounds heavy and sinking 
30 feet per minute, it was possible to pump out the 
excess ballast and bring a submarine into balance in 
the thermocline again. When 12,000 pounds heavy 
and falling 50 feet per minute the vessel was brought 
back into balance by blowing ballast from the nega- 
tive tank which had been flooded. In neither case was 
it necessary to start the motors to regain control. 

It was always possible to check the descent of the 
overweighted submarine and bring it back into the 
stable zone by use of motors and planes. The compen- 
sations which can be made in this way will be con- 
sidered in the following chapter. 

There appears to be no danger of a balanced sub- 
marine getting out of control on falling through a 
thermocline provided constant watch is kept of its 
position in the density layer. Warning will be given 
by the temperature recorded by the bathythermo- 
graph. 

8 5 RUNNING IN BALANCE 

A properly trimmed submarine may not only bal- 
ance with motors stopped when conditions of stable 
buoyancy obtain, it may also proceed at low speeds 
without using the diving planes to control its depth. 
Experiments have indicated that this can be done at 
1 /3 speed, and that during the maneuver, turning the 
vessel with the rudder does not disturb its balance. At 
higher speeds, the submarine tended to ascend, as the 
result of lifting forces occasioned by the hull shape 
and its movement through the water. The critical 
speeds at which this occurs probably depends on the 
strength of the density gradient. 

Even though the stability conditions are not used 
to control the depth, it is evident that a submarine 
operating in a density layer may be more easily kept 


(:(jNi-'iDEXTr \i~ 


50 


STABLE BUOYANCY 


at constant depth with the aid of the planes since each 
deviation from the desired depth sets up forces which 
tend to restore its position. 


The planing forces which arise from the motion of 
a submarine and their relation to the static buoyancy 
forces are discussed in the following chapter. 


TnECTtVin 


Chapter 9 

THE USE OF PLANING FORCES TO CONTROL DEPTH 


W HEN A submarine moves through the water, 
forces arise which act on the hull with a ver- 
tical component. These forces may overbalance the 
static buoyancy forces with which we have been con- 
cerned in the preceding chapters. They may enable a 
submarine to hold constant depth when out of trim 
or to change depth when trimmed for stable buoy- 
ancy. Three groups of forces may be distinguished: 

1. Planing forces due to the hull form. 

2. A vertical component of the propulsive force 
determined by the angle of the hull. 

3. Planing forces due to the angle of the diving 
planes. 

All of these forces increase with the speed of opera- 
tion of the submarine. 

9 1 FORCES DUE TO HULL FORM 

A balanced submarine, which lies horizontal in the 
water (hull angle = 0), tends to rise when under way. 
The greater the speed the greater is the tendency to 
lose depth. If the submarine is running in balance in 
a density gradient the tendency to rise is counterbal- 



Fk.uke 1. Vertical component of propeller thrust of a 
ileet-t)pe submarine as a function of speed and of hull 
angle. It is assumed that the propeller shaft is inclined to 
the water line by 1.5 degrees. 


anced by the decrease in buoyancy which develops as 
the depth changes. Consequently, a submarine may 
frequently run in balance at low speed with the div- 
ing planes held horizontally (at zero angle). The tend- 
ency for the submarine to rise becomes greater* at 
higher speeds. The greater the change in density with 
depth, the less noticeable will this tendency be, and 
the higher the speed at which the submarine will hold 
depth without active control with the diving planes. 

The tendency of a submarine to rise as speed in- 
creases may be attributed in part to planing forces 
due to the form of the hull and superstructure. It is 
probable that the drag of the superstructure tends to 
cause the bow to rise and that the small “up-angles” 
of the hull which result contribute to the loss in 
depth. Furthermore the vertical component of the 
propeller thrust discussed below acts like an increas- 
ing buoyant force as speed is increased.^ 

92 VERTICAL COMPONENT OF THE 
PROPULSIVE FORCE ARISING FROM 
THE HULL ANGLE 

The hull angle of a submerged submarine is meas- 
ured relative to the normal water line of the vessel 
when surfaced. If the water line is horizontal, the 
hull angle is zero. If planing forces are neglected and 
it is assumed that the propulsive force is applied 
parallel to the water line, and at the center of resist- 
ance to forward motion, the vessel may be expected to 
move forward in the direction of the hull angle. If the 
hull is inclined the propulsive force will have a ver- 
tical component, proportional to the sine of the hull 
angle, which will cause the submarine to rise or sink 
as it moves forward. As a result small hull angles will 
cause a moving submarine to change depth rapidly 
in spite of opposing buoyancy forces. 

a In addition to the forces under discussion which arise from 
the forward motion of the submarine, other forces which throw 
it out of trim are set up when the vessel turns in the horizontal 
plane. These cause the submarine to become heavy overall and 
heavy aft. The effect amounts to 6,000 pounds lost buoyancy at 
a speed of 5 knots. It is thought to he due to a low pressure zone 
created beneath the unsymmetrical hull by its horizontal broad- 
side motion. This effect can he compensated for by suitable use 
of the diving planes when turning. 


‘gmxrinF.NTrM,^ 


51 


52 


THE USE OF PLANING FORCES TO CONTROL DEPTH 



Figure 2. Vertical force developed by bow planes, assum- 
ing total area of 124 square feet, as function of their angle 
and the speed. 


Actually the propeller shafts are usually inclined to 
the water line at an angle of about I 1/2 degrees. In 
consequence, if the hull angle is zero a small com- 
ponent of the propulsive force acts upward and tends 
to cause the vessel to rise as it moves forward unless 
counterbalanced by other vertical forces. The vertical 
component of the propulsive force is zero only when 
the hull assumes a down angle of li/^ degrees. The 
vertical component of the propulsive force at various 
hull angles and speeds is estimated to be as shown in 
Figure 1. 

In addition, in most fleet-type submarines the 
thrust of the propellers acts on a point below the cen- 
ter of forward resistance. The thrust consequently 
causes the bow to tend to rise and to alter the hull 


angle in a way which also fa\ors an upward move- 
ment of the vessel. In some of the more recent fleet- 
type submarines the propeller thrust acts approxi- 
mately on the center of resistance and this effect is 
minimized. 

93 PLANING FORCES DUE TO THE 
ANGLE OF THE DIVING PLANES 

The vertical forces developed by the diving planes 
depend upon the angle of the planes and the speed of 
movement. The magnitude of these forces has been 
calculated, using the accepted rudder equations for 
bow planes of 124 square feet combined area, and is 
illustrated in Figure 2. The vertical force developed 
by the stern planes is about 20 per cent less. 

^Vhen the bow and stern planes are adjusted so that 
their vertical moments are balanced, their combined 
force tends to cause the submarine to rise or sink 
without change in hull angle. When the vertical 
moments are not balanced the hull angle changes so 
that the submarine moves upward or downward as it 
is propelled forward. 

In practice, one planesman adjusts the bow planes 
so as to bring the vessel to the desired depth and the 
other manipulates the stern planes to hold the vessel 
at the desired hull angle. In this way the vertical mo- 
ments of the action of the bow and stern planes are 
approximately balanced and both contribute to the 
vertical movement of the vessel. 

94 MAINTAINING CONSTANT DEPTH 

WHEN IN TRIM 

A moving submarine when submerged maintains 
depth and hull angle by balancing the various plan- 
ing and buoyancy forces against one another. The 
vertical forces which arise from movement all tend to 
increase with speed. If the submarine is in good trim, 
so that static buoyancy forces are not involved, 
changes in speed may not disturb the balance of ver- 
tical forces and no adjustment of the angles of the 
diving planes is required as speed increases. This is 
illustrated by data on the plane angles required to 
hold constant depth, secured by a submarine which 
had been brought to trim by balancing, as shown in 
Table 1. 

If the submarine’s hull angle is zero, relatively 
large forces must be developed by the diving planes 
to overcome the vertical components of the propeller 


.MAINTAINING DEPTH CONTROL WHEN OUT OF TRIM 


53 


thrust and the upward forces arising from the hull 
form. This leads to the employment of undesirably 
large plane angles. If the hidl is given a slight down- 


Table 1. Plane Angles Required to Hold a Balanced Sub- 
marine at Constant Depth at \'arions Speeds. USS Catfish. 


Sj)eed 

Htdl 

angle 

Bow plane 
angle 

Stern plane 
angle 

1/3 

0° 

10° dive 

5° dive 

CM 

0° 

12° dive 

4° dive 

Standard 

()0 

12° dive 

4° dive 

Full 

0° 

10° dive 

4° dive 


ward inclination l)y increasing the angle of the stern 
planes the tendency to rise is counterbalanced by the 
vertical component of the propulsive force. The sub- 
marine will then move forward at constant depth 
without the use of the bow planes. The data recorded 
in Table 2 illustrate the angles of hull and stern 
planes retpiired to hold constant depths at dillerent 
speeds, when the bow plane angle is zero. 


Table 2. Hull Angle Required to Hold Constant Depth 
at Various Speeds Without Use of Bow Planes. 


Submarine Speed 

Hull Angle 

Bow plane 
angle 

Stern plane 
angle 

C;atfisii 1/3 

0.50° down 

0° 

7° dive 

2/3 

1.30° down 

0° 

9° dive 

Standard 

1 .75° down 

0° 

7° dive 

Full 

2.50° down 

0° 

7° dive 

Cutlass 1 /3 

1 ..50° down 

0° 

7° dive 

2/3 

1 ..50° down 

0° 

6° dive 

Standard 

1.40° down 

0° 

5° dive 

Full 

1 .40° down 

0° 

6° dive 

Flank 

1.40° down 

0° 

6° dive 


7’he first of these tests indicate that the hull angle 
recpiired to hold depth without the use of the bow 
planes increases with the speed. In the second test, 
however, the speed could be changed without much 
adjustment of the hull angle. In a number of tests 
made in the New London area the latter result was 
obtained also, it being found that speed could be 
changed without adjustment of the diving planes 
when the hull was at 2 to 2i/^ degrees down angle. 
The reason for the difference in behavior in the dif- 
ferent tests is not understood. Many submariners are 
agreed, however, that their vessels are more easily 
controlled when trimmed to secure a small down 
angle of the hull. 


9-^ MAINTAINING DEPTH CONTROL 
WHEN OUT OF TRIM 

If the submarine is not in good trim, the forces 
arising from the diving planes and hull angle are 
employed to overcome the static buoyancy. These 
planing forces increase with speed; the buoyancy 
forces do not. Consequently, changes in speed require 
adjustment of the plane angles. Obviously less angle 
is required on the planes at higher speed to overcome 
a given buoyancy force. \Vhen the submarine is out of 
trim depth is more easily controlled at high speed. 

In the study of the precision of ballast adjustments, 
discussed in Chapter 6, it was found that in 25 dives 
in which good static trims were not obtained because 
of high speed or otherwise, less ballast was shifted 
than was predicted to be required by the bathyther- 
mograph in all but one case. In three-quarters of the 
cases the ballast change was more than 3,000 pounds 
less than the prediction; in extreme cases it was 14,000 
and 16,000 pounds less. 

A number of experiments have been made to de- 
termine the magnitude of the buoyancy force which 
may be overcome by the forces arising from the hidl 
and plane angles at different speeds. The procedure 
is to bring the submarine to trim at low speed and 
then by flooding in or pumping out ballast to deter- 
mine how much of a weight change may be made 
before operation of the diving planes at maximum 








kj 

f 

7 

7 




® / 







40 80 120 160 

SHAFT SPEED RPM 


Fk.ure 3. KIFect of speed and hull angle in counterbal- 
anting excess weight ot a submerged fleet-type submar- 
ine, so as to permit control of depth of operation. 


54 


THE USE OF PLANING FORCES TO CONTROL DEPTH 


angles fails to maintain the depth. The speed is then 
increased and the test repeated by taking on or dis- 
charging more ballast. Some typical results, showing 
the maximum buoyancy change which can be com- 
pensated for under various conditions, are given in 
Table 3 and in Figure 3. 


Table 3. Maximum Buoyancy Change ^Vhich Can Be 
Compensated for by Planing Forces at Different Speeds. 


Sub- 

marine 

Speed 

Bow 

plane 

angle 

Stern 

plane 

angle 

Hull 

angle 

Maximum 

buoyancy 

compen- 

sation 

(pounds) 

COBIA 

1/3 

— 

— 

0° 

2,000 


2/3 

- 

- 

0° 

11,000 

Catfish 

1/3 

25° dive 

0° 

0° 

1,200 


1/3 

25° dive 

7° rise 

1° 

4,000 


2/3 

25° dive 

- 

1 ° 

8,000 

Perch 

1/3 

_ 

_ 

0° 

2,000 


2/3 

— 

— 

0° 

5,000 


Standard 

— 

— 

0° 

9,000 


1/3 

— 

— 

10° 

7,000 


2/3 

— 

— 

10° 

14,000 


Standard 

- 

- 

10° 

38,000 


It is evident that at high speed and with large hull 
angles, buoyancy forces can be overcome which are 
greater than any likely to be encountered as the result 
of the natural variations in the density of sea water. 


Under conditions of emergency, or as a temporary 
expedient in penetrating density layers, advantage 
may be taken of this fact. However, it is usually unde- 
sirable to maintain high speed when submerged for 
very long, because of the drain on the batteries and 
for tactical reasons. Consequently, the importance of 
keeping a submarine in good trim is not decreased by 
the additional control of buoyancy which may be had 
by taking advantage of the planing forces. 

The various forces which determine the behavior 
of the moving submarine are evidently complex and 
great skill is required in operating the vessel to keep 
them in the most effective balance. A submarine 
might be so designed that it could be operated with- 
out using needlessly large plane adjustments to coun- 
terbalance the vertical forces which arise from the 
hull form, and to keep it at a proper hull angle. It is 
evident that present submarines depart widely from 
this ideal and also that the most effective combina- 
tions of hull angle, plane angles, and speed are not 
thoroughly understood. It is believed that a system- 
atic study of the factors controlling the motion of the 
submerged submarine would not only lead to valu- 
able information on how to operate the vessel most 
effectively, and thus supplement the skill which is 
acquired only by long experience, but also might 
serve to establish criteria for the design of more handy 
vessels. 


PLu^Flul.'Til 


Chapter 10 

THE USES OF THE SUBMARINE BATHYTHERMOGRAPH 

IN OPERATIONS 


T he chance of success of any maneuver by a war 
vessel depends on the speed, certainty, and ease 
with which the operation can be carried out; the lat- 
ter is particularly important in an emergency. 

10.1 COMING TO TRIM AT A NEW 
DEPTH 

The submarine bathythermograph® has earned a 
place in the control room if only because it reduces 
the uncertainty of ballast adjustments whenever the 
submarine changes depth. Prior to its introduction 
diving operations resembled somewhat the game of 
blindman’s buff in which the diving officer tried to 
cope with forces which he could not anticipate and 
could only vaguely detect by his feel for the state of 
trim of his vessel. He was aided only by an instrument 
known in the Service as “the seat of his pants.” The 
value of the newer device is attested by the following 
extracts from patrol reports: 

“Many density layers were encountered in this area particu- 
larly off Shiono Misaki and Daio Saki. ... In each case the layer 
necessitated much flooding in to get down and pumping out to 
get back up. The bathythermograph predicted the necessary 
procedure nearly every time. This is a most valuable instrument 
but should be relocated in the Control Room where it can be of 
great assistance to the diving officer.” 

“Density layers were found on both the east and west sides of 
Palau varying in depth from 150 feet to 300 feet. We checked 
the bathythermograph on each deep submergence for informa- 
tion of the Diving Officer which enabled him to adjust his trim 
so that during search following each attack while we were deep 
he never had to pump, blow or increase speed to maintain 
depth.” 

The disadvantage of delays encountered in coming to 
trim during evasion is very real, since the time is 
prolonged during which the noisy operation of the 
pumps and propulsive machinery is required. This is 
evidenced by the following extracts of patrol reports 
from submarines which were not equipped with 
bathythermographs : 

“In the South China Sea . . . while going deep to avoid depth- 
charge attack, it was necessary to flood in 10,000 pounds to re- 
main at 240 feet and not come up, and standard speed had to be 
used until additional water had been taken aboard.” 

a See footnote a. Chapter 1. 


“A density layer was encountered at about 275 feet. Below 
this depth our propeller beats must have been lost to enemy 
A/S vessels though we could still hear their propellers and their 
pinging. Any unusual noises, however, such as blowing or pump- 
ing were immediately picked up by them and drastic action 
followed.” 

Delay is not only disadvantageous in evasion, it 
may be important in more ways than one when re- 
suming attack. Thus: 

“Density layers were experienced twice near Truk. On both 
occasions it was necessary to pump out 3,000 to 5,000 pounds to 
climb at 2/3 speed. Both times this occasioned considerable de- 
lay and no end of irritation to the commanding officer who was 
anxious to get a look.” 

Since the auxiliary ballast pumps can discharge 
only one or two thousand pounds per minute, de- 
pending on the depth, the delays in handling the 
large amounts of ballast mentioned in these reports 
were considerable and well worth keeping at a mini- 
mum. 

The intelligent use of the BT can save much time 
in coming to trim. Most submarine commanders 
make an exploratory dive daily while on patrol to 
obtain information on the density conditions in the 
water in which they are operating. Some even make 
such a dive immediately before an attack, if condi- 
tions permit, so as to be acquainted with the situation 
which will be encountered when time comes to take 
evasive action. Ballast may then be shifted as soon as 
the submarine begins to descend and only small ad- 
justments will be required after the chosen depth is 
reached. 

Even if an exploratory dive has not been made pre- 
viously, the record made during descent gives infor- 
mation of the buoyancy conditions being encoun- 
tered long before they make an effect on the progress 
of the submarine, since when at speed the submarine 
remains under control when several thousand pounds 
out of trim. 

J02 SELECTION OF DEPTH OF 
OPERATION 

Except when operating at periscope depth, the 
exact depth at which a submarine is held is usually 


56 


THE USES OF THE SUBMARINE BATHYTHERMOGRAPH IN OPERATIONS 


DEGREES FAHRENHEIT 



DEGREES FAHRENHEIT 



30 40 50 60 70 80 90 


Fi<;ure 1. Temperature trace showing condition when a 
snl)marine in trim at depth A will also be in trim at the 
greater depths B and C. 


I K.i RF. 2. l emperature trace illustrating the depth at 
which a submarine may balance while using topside lis- 
tening gear to best advantage. 


not tactically important. A knowledge of the density 
distribution in the water will fretpiently permit a 
level to be selected which is advantageous for effi- 
cient operation. 

If a strong density gradient is present there is usu- 
ally one, and sometimes two deeper levels at which 
the buoyancy conditions are the same as at periscope 
depth. If a submarine in trim at periscope depth is 
taken to these levels with the diving planes, it can 
level oft and come to trim again without any change 
in ballast. If the level selected is one of stable buoy- 
ancy, it is not even necessary to guide the submarine 
to the exact depth; if allowed to do so it will find its 
own level of good trim under the action of the forces 
which determine stability. 

Idle depths at which a submarine in trim at peri- 
scope depth will also be in trim on deeper submerg- 
ence are those where the isoballast line which passes 
through the temperature trace at periscope depth 
also crosses the trace at greater depths. Thus, in Fig- 
ure 1 , a submarine in trim at A will also be in trim at 
/i and C. Buoyancy is stable at B and a submarine 
starting to sink from A or brought to any position 
near B under power, will tend to come to the depth of 
B as the result of the buoyancy forces. If the planes 
and power are used to penetrate the density layer to 
reach the depth of C, the submarine will again be in 
trim. 

The advantage of leveling off at the depth, B, at 
which trim is the same as at periscope depth is not 
limited to the ease of silent descent. It also puts the 
submarine in a position to resume aggressive action 
at periscope depth without delays required by ballast 
adjustment. 


Under depth charge attack some advantage is prob- 
ably gained by going below a strong density gradient 
since a well placed charge may tend to “blow” the 
submarine to the surface. The decreased buoyancy of 
the gradient will tend to counteract the upward 
movement of the vessel and may prevent its broach- 
ing. This is, of course, only one of a number of rea- 
sons why submarines go deep in evasive maneuvers. 

10.3 ADVANTAGES OF OPERATING 
IN A DENSITY LAYER 

The BT shows the depths at which a submarine 
will encounter conditions of stable buoyancy. At such 
levels depth control at any speed is easier since the 
sul)marine tends to hold its depth and the diving 
officer and planesmen are under less strain. At low 
speeds the submarine will run in balance, holding its 
depth without use of the diving planes and thus elimi- 
nating any possible sound from that source. This is 
advantageous if the submarine wishes to maneuver at 
creeping speed near the surface in a position ready to 
initiate or resume attack. In deep evasion it is less 
important since the suppression of cavitation sound 
at greater depths makes it permissible to use higher 
speeds without danger of detection by listening 
devices. 

When operating in a density layer, the submarine 
will tend to seek the depth at which it is in trim. If 
trim is imperfect, or if the depth of the density grad- 
ient is changing as the result of internal waves, the 
vessel will tend to rise or sink slowly. If allowed to do 
so, it will soon find its proper level. Consequently, 
when operating under stable conditions, it is much 


c.()\llT)K>rtyr\I. 


MAINTAINING PERISCOPE DEPTH 


57 


better to let the submarine find the level for which it 
is trimmed than to fight the buoyancy forces with the 
planes or to attempt to correct them by ballast ad- 
justment. It has been the practice to operate sub- 
marines at a rigidly controlled depth, quite irrespec- 
tive of the necessity. Actually, it is only at periscope 
depth that exact depth control is usually necessary. 
When running in a density layer at greater depths, 
the aim should be to keep the submarine in water of 
uniform temperature, where it will remain in trim. 
When a density layer is present an understanding of 
the situation can save much noise and effort. 

Balancing in a density layer with motors stopped is 
not favored during evasive action, since there is 
danger of being caught dead in the water by an at- 
tacking escort. There are, however, several situations 
in which balancing may be used to advantage. 

In listening for enemy vessels the cpiieter the sub- 
marine the greater the range over which their pres- 
ence may be detected. By balancing at the very top of 
a temperature gradient, in a position where the top- 
side sonic listening gear is above the gradient and is 
surrounded by isothermal water, the listening ranges 
will be substantially longer than those obtained at 
even slowest speed. (See Figure 2.) When listening 
conditions are good a submarine may cover a greater 
area by this procedure than by sweeping a narrower 
path while moving through the water. 

When forced to remain submerged for long pe- 
riods, there is danger that the batteries will become 
exhausted, necessitating a return to the surface. If a 
sufficient density gradient is present, a submarine bal- 
anced in it will use very little power while waiting for 
an opportunity to return to the surface. 

In an emergency when it is necessary to stop the 
motors for repairs, balancing on a strong density 
layer may permit the submarine to avoid surfacing. 
An impressive instance of the use of this maneuver is 
given in the following extract from a patrol report: 

“At 230-foot depth there was a definite heavy layer that was 
used to advantage when the main induction was flooded. It car- 
ried us for several hours . . . when as much as 5 or 6 thousand 
pounds heavy. It apparently had an effect on sound conditions 
and prevented the DD from any effective sound work as we were 
making considerable noise for a period of over an hour while he 
was nearby and we were below the inversion.” 

104 maintaining periscope depth 

Sudden fluctuations in density sometimes disturb 
the trim of submarines running at periscope depth. 


The vessel may unexpectedly sink or rise from the 
desired depth causing the periscope to be submerged 
or to become dangerously visible. 

A submarine patrolling off Honshu, north of 
Tokyo, reports: 

“Inshore the water was highly stratified with violent horizon- 
tal as well as vertical temperature gradients. Depth control was 
always a problem. ...” 

Another report from off Tokyo emphasizes the rela- 
tion of these disturbances to temperature fluctuations. 

“During normal submerged running at 60 feet temperature 
changes had a marked influence on over-all trim, varying trim 
approximately 800 pounds per degree change in temperature. 
In all cases, however, this figure did not hold true, due perhaps 
to various changes in the density of sea water caused by other 
factors.” 

This vessel had a BT and evidently found it useful to 
anticipate the required ballast compensations. The 
working rule proposed is correct for water of about 
70 F. When the rule failed to hold, it is quite probable 
that the BT thermal element did not record accu- 
rately the changes in temperature of the water sur- 
rounding the hull, since it is located some 15 feet 
above the center of buoyancy and may have pro- 
jected above the thermocline at times. 

The use of the BT in such conditions is again sug- 
gested by the experience of a submarine during a 
shakedown cruise in the Gulf of Maine. 

“It was impossible to obtain a final trim at periscope depth 
for the three days in this area because of the extremely erratic 
changes in the water temperature as shown on the bathythermo- 
graph records. The temperature at 65 feet would often change 
eight degrees in a minute’s time, then in about five minutes 
change just as erratically in the opposite direction. One of the 
junior officers found that if he watched these changes and 
pumped or flooded accordingly, he could maintain trim with- 
out having to lose it first. In other words, the bathythermograph 
told him he was going to lose his trim a short time before he 
actually lost it.” 

Disturbances of this sort are frequently attributed 
to “water pockets.” In the cases described they are 
probably due to internal waves which distort the level 
of the density gradient found in the thermocline. A 
submarine at constant depth cuts through these waves 
becoming lighter as it penetrates a crest and heavier 
as it crosses a trough. 

Internal waves of this character only make them- 
selves felt when the vessel is in a density layer. They 
do not make trouble unless the density layer occurs 
at periscope depth, since this is the only level where 
exact depth control is important. 


^ONFinFA’TTAt^ 


58 


THE USES OF THE SUBMARINE BATHYTHERMOGRAPH IN OPERATIONS 


10.5 the dependence to be placed 
ON BATHYTHERMOGRAPH 
PREDICTIONS 

It needs to be emphasized that the BT is intended 
to assist the diving officer in conducting his opera- 
tions, but that it cannot do his work for him. Its indi- 
cations are predictions of the approximate buoyancy 
conditions he will encounter or is encountering. It 
should be remembered that the instrument, in its 
present form, does not take salinity gradients into 


account, that the water conditions are subject to 
change from time to time and place to place, that the 
recording mechanism is influenced by the water at 
only one point, and that frequently remote from the 
center of buoyancy, and that a submarine is often 
somewhat out of trim at the start of a dive. Conse- 
quently, the BT does not give an exact indication. 
Its predictions have proved useful in achieving ap- 
proximate trim at new levels, but the diving officer 
must still exercise his judgment and skill in the final 
adjustment of buoyancy. 


j^-oisl-fuEN 1 iy> 


Chapter 11 

SUBMARINE SUPPLEMENTS TO THE SAILING 

DIRECTIONS 


T he Sailing Directions issued by the Hydro- 
graphic Office, together with the Coast Pilots 
published by the U. S. Coast and Geodetic Survey, 
give an account of the local conditions which affect 
the navigation of surface ships throughout the world. 
In addition to a description of coastal conditions, 
harbors, port facilities, and aids and hazards to navi- 
gation, they summarize the winds, weather, sea con- 
ditions, and currents which are to be expected in the 
various areas of the ocean. In short, they attempt to 
provide the navigator with a background of informa- 
tion on what he is to expect in the course of his voy- 
age and thus forewarn him and supplement the ob- 
servations which he may make as he proceeds. 

The submarine supplements are intended to ex- 
tend such information in directions which are of pe- 
culiar importance to submarine operations. Thus 
they give an account of the hydrographic conditions 
which inffuence the diving operations of submarines, 
and the characteristics of the water and sea bottom 
which control the length of sound ranges in various 
locations. Since submarines are dependent on dead 
reckoning during submergence, the supplements 
present when feasible more detailed information on 
currents than is found in the Sailing Directions them- 
selves. 

The first supplements were prepared at a time 
when bathythermographs had not yet become gen- 
erally available and some attempt was made to pro- 
vide information on buoyancy conditions which 
might actually be helpful in diving a submarine. Now 
that bathythermographs are in general use this need 
is not so great except in the case of breakdown. 
However, information is provided on the presence 
and strength of salinity gradients which is of imme- 
diate use to submarines equipped with bathythermo- 
graphs since it indicates when the predictions may 
become unreliable and gives a general estimate of the 
correction which should be applied on account of the 
salinity gradient. 

A second way in which the supplements may be 
useful to the submarine on patrol is in showing 
whether the conditions presently encountered are 


liable to change, either because the area of operation 
is one of variable hydrography, or because the vessel’s 
course is taking it into a region where the situation is 
different. Knowledge of this sort should determine 
the frequency with which exploratory dives are made. 
It is particularly important that a submarine run- 
ning on the surface should be aware of changing 
buoyancy conditions since difficulty may be experi- 
enced in coming to trim on submerging if the density 
of the water at periscope depth changes in the course 
of the run. 

In addition to these immediate uses the informa- 
tion in the supplements has an intangible but very 
real value in giving the submariner an advance pic- 
ture of the conditions he is likely to meet during a 
patrol and thereby preparing him for difficulties. The 
supplement thus takes the place of the man who has 
been there before. 

The supplements contain information which 
should also be of great value in strategic planning. 
The information supplied concerning sound ranging 
conditions make it possible to distribute available 
forces in such a way as to take advantage of the im- 
munity from detection during evasion which is af- 
forded by favorable temperature gradients. There is 
some indication that the Germans took advantage of 
this possibility in planning their submarine cam- 
paigns in the Atlantic and very good evidence that 
our own antisubmarine operations were greatly 
handicapped in areas where sound conditions were 
favorable to the German submarines. Even within 
the limits of an assigned patrol area, local conditions 
such as the character of the bottom may permit a 
submarine to choose the exact position of operation 
so as to be at an advantage. 

11 1 AREAS COVERED BY THE 

SUPPLEMENTS 

The only area in the Atlantic which has been cov- 
ered by a submarine supplement is the Bay of Biscay.^ 
A preliminary supplement on the eastern North 
Atlantic was prepared for the National Defense Re- 


’^l^ONFIDENTfli? 


59 


CO 


SUBMARINE SUPPLEMENTS TO THE SAILING DIRECTIONS 


70° 80° 90° 100° 110° 120° 130° 140° 150° 160° 170° 180° 170° 160° 



search Committee, but was not published due to 
changing war conditions.^ Supplements® covering 
conditions for the entire year have been published for 
three areas in the Pacific where American submarines 
have undertaken extensive operations, namely, the 
South China Sea, the western tropical Pacific, and the 

a Preliminary submarine supplements were published for 
some of the seasons in these areas. These are listed in the 
bibliography. 


area surrounding the Japanese Empire.^-^ These areas 
overlap slightly. (See Figure 1.) 

It seems highly desirable that additional supple- 
ments be prepared for all the oceanic areas of the 
world. There is immediate need for supplements 
covering the various training areas in the United 
States, such as off Portsmouth, New London, Key 
West, San Diego, and the Panama Canal. These 
would not only serve to acquaint men in training 


[TiXflDEN 




INFORMATION SUPPLIED 


61 


with the uses of the supplements, but would also 
give them a better understanding of the conditions 
which they encounter during their training. In addi- 
tion, in conducting tests it is frequently important to 
select locations where particular sound or buoyancy 
conditions occur. Much time would be saved and 
better tests would result if such information on local 
hydrography were conveniently available. 

112 INFORMATION SUPPLIED 

Under the heading Subsurface Climate the general 
hydrographic conditions which influence diving and 
sound transmission in the various natural areas are 
described. Typical BT records and extracts from 
patrol reports from the area serve as illustrations. 
The Japanese Empire Area is divided into ten sub- 
areas for this purpose; in the South China Sea Area 
and the Western Tropical Pacihc Area, the subsur- 
face climate is discussed as a whole. 

Under Subsurface Forecasting some account is 
given of such factors as the weather, currents, and the 
run-off from land, which may enable changes in the 
situation to be predicted. Charts are included show- 
ing the character of the bottom or giving an index to 
the available bottom sediment charts of the area. In- 
formation on the transparency of the water is sup- 
plied where available. The most useful information, 
however, is given in a series of charts which show the 
average conditions for all seasons of the year which 
affect certain basic operations. The charts in the 
Supplement for the Japanese Empire Area cover the 
following features. 

11.2.1 Surface Current Charts 

Streamlines 

These charts show the average resultant direction 
and velocity of the major surface currents. They do 
not include tidal current. (See Figure 2.) 

Surface Currents — Roses 

The amount of time the currents flow in different 
directions and at different speeds are shown. (See 
Figure 3.) 

Buoyancy Charts 

The data on all buoyancy charts are given for a 
submarine having a submerged displacement of 2,400 


tons and a compression of 2,000 pounds per 100 feet, 
and are in terms of pounds of ballast to be pumped or 
flooded. 

Buoyancy Change Due to Salinity Gradient 

These charts show the change in buoyancy due to 
the salinity gradient between periscope depth and 
some stated level of deep submergence (300 or 450 
feet). They may be used to learn whether the BT 
prediction will be dependable or whether an allow- 
ance should be made for the effect of salinity in pre- 
dicting ballast change. The buoyancy corrections are 
given in terms of ballast to be flooded, and are either 
to be added to the amount flooded, or subtracted 
from the amount to be pumped, as predicted by the 
bathythermograph. (See Figure 4.) 

Buoyancy Change Due to Density Gradient 

These show average ballast changes due to both 
temperature and salinity gradients between periscope 
depth and some stated depth suitable for deep sub- 
mergence (300 or 450 feet). They show whether strong 
density layers are likely to be encountered and indi- 
cate the total ballast change which may be required 
in deep submergence. (See Figure 5.) 

Sharpness of Density Layer 

The maximum sharpness of the density layer and 
its approximate depth are shown. The purpose of 
this chart is to show the depths at which density 
layers exist within the range of submarine operations 
and the security of balancing within these layers. (See 
Figure 6.) 

Size and Thickness of the Density Layer, August 

This chart shows the depth to the top and the 
depth to the bottom of the main density layer, and 
the size of the layer in terms of amount of ballast 
which must be flooded to penetrate the layer. It sup- 
plements the preceding one in showing the existence 
of balancing conditions and the range of depth 
through which such conditions can be expected. It 
applies only to the month of August when the most 
noticeable gradients occur. (See Figure 7.) 

Sonar Range Charts 

Periscope Depth, Echo Range, and Effect of Wind 

These charts show the frequency in which maxi- 
mum echo ranges at periscope depth are less than 




62 


SUBMARINE SUPPLEMENTS TO THE SAILING DIRECTIONS 



Figure 2. A part of Chart Ic from the Submarine Supplement to the Sailing Directions, Japanese Empire Area, H. O. 
Pub. No. 231, illustrating surface currents as streamlines. 


INFORMATION SUPPLIED 


63 



Figure 3. A part of Chart 2(1 from the Submarine Supplement to the Sailing Directions, Japanese Empire Area, H, O. 
Pul). No, 231, illustrating surface currents by means of roses. 



64 


SUBMARINE SUPPLEMENTS TO THE SAILING DIRECTIONS 


115 " 


120 


125 - 


130 


135 


140 


145 


50 “ 


45 “ 


CHART 3c 

BUOYANCY CHANGE DUE TO SALINITY GRADIENT 
PERISCOPE DEPTH TO 300 FEET 
August 

CONTOURS show probable INCREASE IN BUOYANCY due to change 
in SALINITY between PERISCOPE DEPTH and 300 FEET, measured in 
thousands of pounds for a submarine of 2400 tons submerged displace- 
ment. Contours in WATER LESS THAN 300 FEET DEEP (YELLOW) 
show average salinity gradient between PERISCOPE DEPTH and 150 
FEET. Gradients in shallow water are variable. NUMBERS IN ITALICS 
show MAXIMUM RECORDED BUOYANCY CHANGE due to salinity be- 
tween PERISCOPE DEPTH and 150 FEET. 

I I FLOOD 0-4000 lbs. | | FLOOD 4000-8000 lbs. 

This chart shows salinity corrections to be added 
to buoyancy adjustments for temperature as indicated 
by the bathythermograph. 

For fuller explanation, see page 46. 



115 * 


120 * 


125 ' 


130 * 


135 ' 


140 


145 


Figure 4. Chart 3c from the Suljmarine Supplement to the Sailing Directions, Japanese Empire Area, H. O. Pub. No. 
231, illustrating buoyancy change due to salinity gradient between periscope depth and 300 feet. 


INFORMATION SUPPLIED 


65 



Figure 5. A part of Chart 4c from the Submarine Supplement to the Sailing Directions, Japanese Empire Area, H. O. 
Pub. No. 231, illustrating buoyancy change due to density gradient between periscope depth and 300 feet. 



66 


SUBMARINE SUPPLEMENTS TO THE SAILING DIRECTIONS 



Figure 6. A part of Chart 5c from the Submarine Supplement to the Sailing Directions, Japanese Empire Area, H. O. 
Pub. No. 231, illustrating sharpness of the density layer. 


INFORMATION SUPPLIED 


67 



Figure 7. A part of Chart 6 from the Submarine Supplement to the Sailing Directions, Japanese Empire Area, H. O. 
Pub. No. 231, illustrating size and thickness of the density layer. 



68 


SUBMARINE SUPPLEMENTS TO THE SAILING DIRECTIONS 



CHART 7d 

PERISCOPE DEPTH ECHO RANGE AND EFFECT OF WIND 
August 

COLOR shows MAXIMUM ECHO RANGE AT PERISCOPE DEPTH, 
measured in terms of percent of time range is less than 1500 yards 
when WIND IS LESS THAN FORCE 6. 

I I 0- 25 (Ranges generally over 2000 yds.) 


25- 50 (Ranges generally over 1500 yds.) 


I I 50- 75 (Ranges generally less than 1500 yds.) 

□ 75-100 (Ranges generally less than 1000 yds.) 

Over ROCK bottom, ranges will be shorter than these figures. 


CONTOURS show percent of time WIND IS FORCE 6 OR GREATER. 

PAIRS OF NUMBERS: First number is percent of 
time periscope depth echo range is shorter than 1500 . 
yards at night, and second number is percent of time 
it is shorter in afternoon. Difference between num- 
bers is caused by “Afternoon Effect”. 

For fuller explanation, see page 49. 55 - 


WO-90 


5 T0 10 


115" 


120 


125 


130 


135 


140 


145" 


120 ® 


125" 


130® 


135® 140® 145® 


-75 


15-25 


Figure 8. A part of Chart 7d from the Submarine Supplement to the Sailing Directions, Japanese Empire Area, H. O. 
Pub. No. 231, illustrating periscope depth echo range and effect of wind. 


INFORMATION SUPPLIED 


69 



CHART 8d 
ASSURED RANGE 
August 

CONTOURS and numbers give probable DEPTH OF ASSURED RANGE, 
that is, the depth at which maximum echo range is SHORTEST, and 
therefore the depth at which a submarine can best avoid detection from 
echo ranging. In shallow water, except over MUD bottom, range is ap- 
proximately the same at all depths. Numbers In shallow water apply 
only over MUD bottom. Spotty areas on the chart indicate highly vari- 
able conditions due to patchy bottom In shallow water. Check actual 
conditions frequently with bathythermograph observations and bottom 
sediment charts. 

COLOR shows average ASSURED RANGE. 

I I Less than 1000 yds. | | 1500 to 2000 yds. 


I I 1000 to 1500 yds. 

For fuller explanation, see page 49 


:SVARIABILITY 
OF DEPTH CONTOURS:: 


H High variability 
M Moderate variability: 
L Low variability 


20 ® 


115 ** 


120 


125 


130 


140® 


145 


135 


150 

^^5 TO 150 


140 ® 145 ® 


115 ° 


120 ° 


125 ^ 


130° 


135° 


Fk;ure 9. A part of Chart 8d from the Submarine Supplement to the Sailing Directions, Japanese Empire Area, H. O. 
Pub. No. 231, illustrating assured range. 



70 


SUBMARINE SUPPLEMENTS TO THE SAILING DIRECTIONS 



CHART 9c 

ASSURED RANGE AT PERISCOPE DEPTH 
August 

CONTOURS and numbers show percent of time MAXIMUM ECHO 
RANGE is shorter at PERISCOPE DEPTH than at any greater depth, due 
to the presence of negative temperature gradients extending from the 
surface of the water downward. Assured Range and reliable ping range 
under such conditions generally are less than 1000 yards. 

COLOR shows percent of time MAXIMUM ECHO RANGE is the same 
at all depths. This is due to three conditions: (1) deep isothermal water 
which causes ranges of more than 2000 yards, (2) strong winds which 
cause relatively short ranges (see Chart 7d), and (3) type of bottom which 
causes variable ranges in shallow water. 


LESS THAN lO 


115 ” 


120 


125 


130 


135 


140 


145 


20 ° 

115 ° 


120 ° 


125 ° 


130 ° 


135 ° 


140 ° 


145 ° 



0- 25 % 



1 1 

25- 50% 



50- 75% 


75-100% 


This chart shows the percent of time when echo , 
ranges at periscope depth are no greater than they 
are at any greater depth, and a submarine will gain . 
no protection from echo ranging by going deep. 

For fuller explanation, see page 50. 


Figure 10. A part of Chart 9c from the Submarine Supplement to the Sailing Directions, Jajiancse Empire Area, 
H. O. Pub. No. 231, illustrating assured range at periscope depth. 


INFORMATION SUPPLIED 


71 


1,500 yards. They do not apply when the wind force is 
6 or more, under which condition shorter ranges are 
to be expected. Contours also indicate how frequently 
wind forces of 6 or more are to be expected. The 
charts thus show the probability that local conditions 
will favor undetected operations at periscope depth. 
(See Figure 8.) 

Assured Range 

These charts show the depth at which maximum 
echo ranges are probably shortest and the ranges to be 
expected at that depth. They consequently indicate 
the depths at which a submarine can best avoid de- 
tection by echo ranging and the relative chances of 
detection when at such depths in the various regions. 
(See Figure 9.) 

Assured Range at Periscope Depth 

This chart shows the percentage of time that echo 
ranges are shorter at periscope depth than at any 
greater depth. Since unusually poor sound conditions 
usually accompany this condition the chart indicates 
the probability that submarines will be at an advan- 
tage during aggressive action, both during attack and 
evasion. (See Figure 10.) 

11 3 SOURCES OF DATA AND 

RELIABILITY OF PREDICTIONS 

The charts in the supplements were constructed 
from two types of data: 

1. Over 70,000 serial temperature observations 
from the western Pacific including some salinity ob- 
servations. These were taken largely by the Japanese 
and the largest number of the observations are from 
Japanese waters. 

2. Several thousand BT records taken both by 
American submarines and antisubmarine vessels. 

There are some objections to the use of either of 
these types of data if highly accurate charts are de- 
sired. Serial temperatures are usually quite precise 
but they do not give a complete picture of the sub- 


surface temperature gradients because the tempera- 
ture is recorded only at a series of separate depths. 

Bathythermograph records give a continuous tem- 
perature profile, but frequently the temperature is 
subject to a systematic error of as much as 5 degrees 
because the recorder is not correctly adjusted. In 
compiling charts showing the temperature at various 
depths using BT data, an incorrect result may be ob- 
tained. Since temperature differences between the 
depths in question determine the buoyancy change 
which will be encountered in diving, these errors do 
not have a practical effect upon the usefulness of the 
BT. Similarly BT data may be employed to prepare 
charts showing the difference in temperature between 
two depths in spite of the usual errors in adjusting the 
instrument. A more important objection to the use of 
BT records secured by Service vessels is that the geo- 
graphic locations given with the records are often 
unreliable. This is caused by lack of precision in 
keeping the data, and is a personnel problem diffi- 
cult to solve during time of war. 

The buoyancy charts in the supplements were con- 
structed largely on the basis of recorded serial tem- 
peratures and salinities. There are large areas where 
the data are scanty, especially that on salinity. Some 
of the charts contain a small inset to indicate the 
variability of the data on which they were con- 
structed. In areas where the data had a high varia- 
bility the average conditions shown are generally 
less reliable than in areas having low variability. 

In the preparation of the charts it was necessary to 
make the best of the available information and fre- 
quently to resort to general oceanographic theory to 
fill in areas where data was inadequate or even to 
ignore some data which conflicted with theory. While 
this was doubtless the most expedient procedure, 
more useful charts could be constructed if special 
surveys were made for the purpose in critical areas 
where general oceanographic information is insuffi- 
cient. In particular, more detailed information is 
needed concerning the salinity distribution and con- 
cerning the normal variability of the conditions, since 
these are the two most useful items covered in the 
supplements. 


TcOM'IDI'.M lA^ 


Chapter 12 

THE PROBLEM OF RESUBMERGENCE 


T he discussion of the control of buoyancy in the 
preceding chapters has always started with the 
assumption that the submarine was in trim at peri- 
scope depth or some other depth of submergence. The 
control of buoyancy on changing depth is simply a 
matter of adjusting ballast to compensate for the 
effects which result from compression and from the 
changing density of the sea water. When a surfaced 
submarine submerges, difficulty is frequently en- 
countered in bringing the vessel to trim at the desired 
depth quickly. The submarine may find itself so 
heavy that it is forced to blow ballast from the safety 
tank to avoid sinking or it may be so light that it can- 
not get down until it has flooded additional water 
into the auxiliary tanks. Neither condition is com- 
patible with efficient operation. 

The difficulty arises from two sources. There is no 
exact method of judging the change in weight of a 
submarine due to consumption of fuel, stores, and 
ammunition while it is on the surface; also, there is 
no convenient means of measuring in advance the 
buoyancy of the water which will surround the sub- 
marine when it reaches the desired depth of 
submergence. 

Careful estimates are made of the changes in 
weight which occur while submarines are on the sur- 
face. If the surface run is not too long these estimates 
are sufficiently precise to permit compensation to be 
made before submerging. If longer runs are made on 
the surface, or if the submarine has docked and taken 
on supplies, larger errors may arise. For this reason 
submarines commonly make a dive to establish trim 
soon after leaving port, and repeat the procedure at 
least daily while cruising or on patrol. 

I2.I THEORY OF RESUBMERGENCE 

The difficulties which arise as the result of hydro- 
graphic factors may best be discussed after consider- 
ing the general theory of resubmergence. 

Let Wi = weight of submarine exclusive of main 
ballast water. 

w = weight of main ballast water. 

V = displacement of submarine. 


V = displacement of main ballast water. 

p® = density of water surrounding submarine 
at periscope depth at point A, where 
original trim obtains. 

= density of water surrounding submarine 
at periscope depth at point B, where trim 
is desired on resubmergence. 

pa/w = density of water in main ballast tanks at 
point A. 

pb/w = density of water in main ballast tanks at 
point B. 

It is desired to find AW, the change in ballast re- 
quired to establish trim at periscope depth at point B. 

At point A where trim obtained at periscope depth 
before surfacing: 

TFi -f = Fp®. (1) 

At point B after submerging to periscope depth, good 
trim will obtain when: 

AIT + TFi + r^p^/'® = Vp^. (2) 

Subtracting (1) from (2): 

ait = v { p ^ - P®) - v { p ^/^^ - p®/*^'). (3) 

The ballast adjustment required to compensate for 
the change in density of the water between the point 
of surfacing and resubmergence depends upon the 
change in density of the water at periscope depth and 
the difference in density of the water in the main 
ballast tanks before surfacing and after resubmerg- 
ence. The practicability of applying the relation 
shown in equation (3) depends on the kind of hydro- 
graphic conditions which may be encountered. 

12 2 resubmergence when vertical 

DENSITY GRADIENTS ARE SMALL 

When density gradients present between the sur- 
face and periscope depth at both the point of surfac- 
ing and resubmergence are small or absent, the den- 


72 


tcOXFlDKX iTaTT 


RESUBMERGENCE WHEN VERTICAL DENSITY GRADIENTS ARE LARGE 


73 


sity of water in the ballast tanks will be practically 
the same as that surrounding the vessel, and equation 
(3) may be written: 

aW = (F- v)(p^ - p«). (4) 

Furthermore, measurement of the density of the sur- 
face water may be used as the value of p^, the density 
at periscope depth at the point of submergence. The 
surface density at the point of surfacing may also be 
substituted for p®, the density at periscope depth, 
though this value can be measured from the sub- 
merged submarine. 

When these simplifications are permissible, the 
following formula may be used in compensating for 
changes in the density of the water encountered by a 
submarine of 2,400 tons submerged displacement 
while cruising on the surface. 

AIF = 4 X lO^Ap. 

This formula assumes that the ballast water displaces 
one-fourth the displacement of the submerged sub- 
marine. It means that 4,000 pounds of ballast should 
be flooded for each increase in density of 0.001. 

When the absence of density gradients near the 
surface permits the use of the foregoing rule, it may 
be useful to determine the density of the water with a 
hydrometer, especially when the horizontal density 
change is large. A submarine has reported that in 
passing through the Panama Canal, where the differ- 
ence in density on the two sides is about 0.002, the 
hydrometer predicted exactly the compensation re- 
quired for resubmergence. A submarine equipped 
with the CXJC buoyancy recorder has found the indi- 
cations of this instrument helpful in compensating 
for the difference in density between Long Island 
Sound, where trim dives were made, and the more 
saline water encountered in offshore test areas. On 
the other hand, observations made in the course of 
daily trim dives during a cruise from New London to 
Panama indicated that errors in estimating the weight 
change of the submarine due to consumption of fuel 
and stores during a 24-hour run were larger than the 
corrections for the changing density estimated from 
hydrometer readings, and consequently no advantage 
was gained from these corrections. 

It is not reliable to estimate the change in density 
from the temperature of the surface waters, because 


horizontal density gradients are more likely to result 
from salinity differences than from temperature. 

12 3 RESUBMERGENCE WHEN VERTICAL 
DENSITY GRADIENTS ARE LARGE 

If the density of the water changes markedly be- 
tween the surface and periscope depth, the simplified 
rule discussed above is not reliable, particularly if the 
gradient is great at the point of resubmergence. All 
the terms in equation (3) are significant and should 
be evaluated to secure a dependable prediction. Un- 
fortunately it is not practical to do this. 

The density of the water at periscope depth at the 
point of surfacing, p®, can be measured from the sub- 
marine before it surfaces, but there is no convenient 
way of evaluating p^ the density of the water at peri- 
scope depth where trim is desired after resubmerging. 
This could be determined with an instrument such as 
the surface vessel bathythermograph which could be 
lowered from the surfaced submarine. It has not 
seemed desirable to resort to this procedure which 
would add another item to submarine equipment. 
The water which will fill the main ballast tanks on 
resubmergence enters the tanks at a depth of about 15 
feet. The density of this water, p^/^, can be obtained 
with sufficient accuracy from a suitable water line 
while the submarine is surfaced. The density of the 
water which is in the main ballast tanks before sur- 
facing, p®/% is more difficult to evaluate. If the sub- 
marine has been at periscope depth for some time, 
and the density gradient is due largely to temperature 
effects, the water in the main ballast tanks may be 
assumed to be in thermal equilibrium with the sur- 
rounding sea water and its density may be taken as 
the same as p®, the density at a depth of, for example, 
55 feet. On the other hand, if the submarine has re- 
cently submerged, as will be the case if the usual trim 
dive is made in the course of a cruise, the water in the 
main ballast tanks will be similar to that at about 15 
feet below the surface. 

These uncertainties, particularly the difficulty in 
determining the density at periscope depth in ad- 
vance of submerging, make it impossible at present 
to predict the correct ballast compensations under 
the very conditions in which difficulty is most likely 
to be encountered. 

Submarines should be particularly cautious when 
resubmerging in the water of low density which is 
found along coasts where the surface sea water is di- 


CO.NF 


74 


THE PROBLEM OF RESUBMERGENCE 


luted with river water. In such situations very strong 
salinity gradients often occur between the surface and 
periscope depth. If a submarine, which has surfaced 
after obtaining trim offshore, enters such an area and 
attempts to compensate its weight on the basis of 
measurements of the density of the water near the 
surface it will be too light when it descends into the 
denser water beneath the surface. It will be in danger 
of broaching when the negative tank is blown when 
leveling off to come to trim. On such an occasion it 
will be necessary to retain an excess of ballast in the 
negative tank until a compensating amount of ballast 
is flooded into auxiliaries. 

The following rules have been developed to guide 
a submarine which is in trim and measures the den- 
sity of the water at periscope depth at the point of 
surfacing and again determines its density at a depth 
of about 15 feet at the point where it expects to 
resubmerge. 

1. When the density at 15 feet is greater than the 
density at periscope depth at the previous point of 
surfacing, the submarine will be light if it dives unless 
additional ballast is flooded. It is advisable to run 
with the boat heavy. 

2. When the density at 15 feet is the same as the 
density at periscope depth at the previous point of 
surfacing, the submarine may be light or in trim if it 
dives. It may be advisable to run with the boat heavy. 

3. When the density at 15 feet is less than the den- 
sity at periscope depth at the previous point of sur- 
facing, diving conditions are unpredictable. Where 
there is a strong temperature or salinity gradient at 
shallow depths, difficulty may be encountered on sub- 
mergence. Since conditions cannot be predicted at 
periscope depth it may be advisable to go down on 
the planes at high speed, and to make ballast adjust- 
ments according to the feel of the boat after greater 
depths are reached. 

12 4 SUBMARINE SUPPLEMENTS AS AN 
AID IN RESUBMERGENCE 

It might be thought that the Submarine Supple- 
ments to the Sailing Directions could give useful in- 
formation on the density gradients existing between 


the surface and periscope depth and that this infor- 
mation could be used in estimating the ballast ad- 
justments required for resubmergence. Unfortun- 
ately in the situations where these strong gradients 
occur, the conditions are likely to be very variable. 
Quantitative information consequently cannot be 
given. For example, a study of the problems of re- 
submergence in the Yellow Sea, made by the Scripps 
Institution of Oceanography, has shown that for re- 
submerging after a run between two stations 10 miles 
apart, the ballast compensation estimated according 
to equation (3) was as follows: 

August 11, 1932 Flood 1,500 pounds 

August 9, 1933 Flood 16,000 pounds 

August 1,1934 Flood 750 pounds 

August 17-18, 1935 Pump 3,875 pounds 

This variability makes it impossible to furnish sub- 
marines with quantitative predictions for resubmerg- 
ence conditions in such areas as the Yellow Sea. 

The earlier editions of the submarine supplements 
contained maps showing the horizontal distribution 
of density in the sea’s surface, which were intended to 
indicate whether important changes in buoyancy 
would be encountered following a surface run. These 
charts have been omitted from later editions because 
it appeared that such changes did not occur in large 
areas of the ocean and because of the difficulty in 
taking account in a quantitative way of the effects of 
the vertical density gradients. Since submarines can- 
not secure the needed information for themselves it is 
important that the supplements continue to supply 
the best advice possible for resubmergence. It should 
at least be possible to show: 

1. The areas and seasons where no compensation 
is required for horizontal changes in density. 

2. The areas and seasons where compensation may 
be made on the basis of measurements of surface 
density because of the absence of vertical density 
gradients. 

3. The areas and seasons where strong vertical 
density gradients are likely to create difficulty in 
resubmergence. 



GLOSSARY 


BALANCING. Allowing a stationary submarine to float in a 
density layer. 

BOURDON TUBE. A flattened curved tube which tends to 
straighten out under internal pressure, used as the driving 
element in pressure and temperature gauges. 

BT. Bathythermograph. 

BUOY.\NCV. As used in this volume, the net buoyancy, or the 
difference between the weight of the water displaced by a 
vessel and the weight of the vessel. 

COMPRESSION. A coefficient expressing, in pounds per hun- 
dred feet, the combined effect on submarine buoyancy of the 
compressions of sea water and of the vessel with increasing 
depth. It is always negative in value. 

DENSITY GRADIENT. Change in density with depth. 

DENSITY LAYER. A layer of water in which density increases 
with depth enough to increase the buoyancy of a submarine. 
(Submariner’s term for a density gradient.) 


ISOBALLAST LINES. A set of lines, on the SBT chart, start- 
ing from a set of selected points on the temperature scale and 
passing through all points for which the net change in buoy- 
ancy, resulting from changes in water temperature and depth, 
is zero for a submarine of a given compression. 

SALINITY. Number of grams of salt per thousand grams of sea 
water, usually expressed in parts per thousand. 

SALINITY GRADIENT. Change in salinity with depth, ex- 
pressed in parts per thousand per foot. 

SBT. Submarine bathythermograph. 

STABILITY. The resistance to overturn or mixing of the water 
column, resulting from the presence of a density gradient. 

STOP TRIM. The condition of trim, when net buoyancy is 
zero, whereby a stationary submarine can maintain its depth. 

TEMPERATURE GRADIENT. Change of temperature with 
depth, expressed in degrees F per foot. 

THERMOCLINE. A layer of water in which temperature de- 
creases with depth; a negative temperature gradient. 

TRIM. The adjustment of submarine buoyancy. 


CO NblDUN lI? 


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BIBLIOGRAPHY 


Numbers such as Div. 6-501.1 1-M8 indicate that the document listed has been microfilmed and that its title appears in the 


microfilm index- printed in a separate volume. For access to 
Navy agency listed on the reverse of the half-title page. 

1. Instructions for the Installation, Care and Use of the Sub- 
marine Bathythermograph Types CTB 40079 and CTB 
40171, Contract 98660, BuShips, WHOI, and the Bristol Co. 

Div. 6-501.1 1-M8 

2. Instructions for the Installation, Care and Use of the Sub- 
marine Bathythermograph Type CTB 40131. NXss-24692, 
WHOI, Bristol Co., BuShips, and NDRC. Div. 6-501 .1 1-M9 

3. Description and Operating Instructions for Model CXJC, 

OEMsr-31 (Subcontract 1), NDRC 6.1-sr31-1735, February 
1945. Div. 6-501.1 1-M4 

4. Navy Model OCO Submarine Bathythermograph Equip- 
ment, Instruction 79001 R, Issue I, Contract NXss 8740, 

Brown Instrument Co., Feb. 15, 1945. Div. 6-501.1 1-M5 

5. Use of Submarine Bathythermograph Observatio}is, Bu- 
Ships and NDRC, May 1943. 

6. Use of Submarine Bathythermograph Observations, Nav- 
Ships 943-F, BuShips and NDRC, August 1943. 

7. Lecture Notes on Use of Submarine Bathythermograph, 

Bristol Co., January 1944. Div. 6-501. 11-M3 

8. Use of Submarine Bathythermograph Observations as an 
aid in Diving Operations. Supplement to NA VSHIPS 943-F, 
NavShips 900,018, BuShips and NDRC, March 1944. 

9. Use of Submarine Bathythermograph Obsen'ations. Part 4. 
Diving, NavShips 900,069, BuShips, April 1945. 

10. Lecture Notes on the Use of the Submarine Bathythermo- 
graph, \VHOI and Com Sub-Lant, July 1945. 

Div. 6-501.1 1-M6 

11. Submarine Supplement to Hydrographic Office Publication 
No. 133, Sailing Directions for the Bay of Biscay, Hydro- 
graphic Office, June 1943. 

12. Late Summer Hydrographic Conditions in the Japanese 

Area, UCDWR Report U85, I’reliminary Submarine Sup- 
plement to Hydrographic Office Publication 123: Asiatic 
Pilot, Vol. II, The Japanese Archipelago. BuShips and 
NDRC, July 1943. Div. 6-501. 2-M2 

13. Sailing Directions for the West Coasts of Spain, Portugal, 

and Northwest Africa and Off-lying Islands, Submarine 
Supplement to Hydrographic Office Publication 134, 
WHOI, January 1944. Div. 6-501.3I-M1 

14. Summer Submarine Supplement to Hydrographic Office 
Publications Nos. 122, 123, and 124, The Japanese Empire 
Area, June, July, and August, Misc. 11,381, Hydrographic 
Office, May 1944. 

15. Submarine Supplement to Hydrographic Office Publication 
No. 165. Western Pacific Area, July, August, and September. 
Misc. 11,418, Hydrographic Office, June 1944. 


COXFII) 


the index volume and to the microfilm, consult the Army or 


16. Submarine Supplement to the Sailing Directions, The Japa- 
nese Empire Area, September-December, Misc. 11,381-A, 
Hydrographic Office, July 1944. 

17. Submarine Supplement to the Sailwg Directions, The West- 
ern Pacific Area, September-December, Misc. 11,418-2, Hy- 
drographic Office, August 1944. 

18. Submarine Supplement to the Sailing Directions, South 
China Sea Area, November- April, H. O. Misc. 11,530-1. 
Hydrographic Office, October 1944. 

19. Submarine Supplement to the Sailing Directions, Japanese 
Empire Area, January-March, Misc. 11,381-B, Hydrographic 
Office, November 1944. 

20. Submarine Supplement to the Sailing Directions, Westerti 
Tropical Pacific Area, January-March, Misc. 11,418-3, Hy- 
drographic Office, November 1944. 

21. Submarine Supplement to the Sailing Directions, Japanese 
Empire Area, Pub. 231, Hydrographic Office, May 1945. 

22. Submarine Supplement to the Sailing Directions, South 
China Sea Area, Pul). 232, Hydrographic Office (in press). 

23. Submarine Supplement to the Sailing Directions, Western 
Tropical Pacific Area, Pub. 233, Hydrographic Office (in 
press). 

24. Resubmergence Problems in the Yelloiu Sea, Technical Re- 
port 3, Scripps Institution of Oceanography, Tan. 19, 1945. 

Div. 6-501. 32-M2 

25. A Slide Rule to Facilitate Buoyancy Computations, Tech- 
nical Report 5, Scripps Institution of Oceanography, Jan. 

29.1945. Div. 6-501. 321-M2 

26. Density Gradients in the Nortlncestern Pacific, August, 

Technical Report 6, Jan. 23, 1945. Div. 6-501. 322-M4 

27. Vertical Buoyancy Differences due to SaVuiity in the Yelloiu 
and East China Seas, Technical Report 8, Scripps Institu- 
tion of Oceanography, Feb. 20, 1945. Div. 6-50I.32TM3 

28. Methods Employed in the Construction of Average Buoy- 
ancy Charts for the Submarine Supplements, Technical Re- 
port 12, Scripps Institution of Oceanography, May 19, 1945. 

Div.6-50I.321-M5 

29. A Method for the Determination of the Relative Subsurface 

Currents from Profiles of Relative Buoyancy, Technical Re- 
port 13, May 12, 1945. Div. 6-501.321-M4 

30. Submarine Operational Conditions in the Kii Suido, Tech- 
nical Report 14, Scripps Institution of Oceanography, May 

24.1945. Div. 6-501. 31 -M3 

31. Hydrography of the Formosa Strait, Technical Report 16, 

June 19, 1945. Div. 6-501. 2-M5 


:\ 1 1 ; 


77 


78 


BIBLIOGRAPHY 


32. Hydrography and Submarine Operating Conditions in Tsu- 
garu Kaikyo and its Eastern Approach, Technical Report 
17, Scripps Institution of Oceanography, Aug. 9, 1945. 

Div. 6-501.31-M4 

33. The Waters off the South Coast of Japan, Longitudes 131°- 

136° E. Submarine Operating Conditions, Technical Report 
19, Aug. 20, 1945. Div. 6-501.31-M5 

34. Internal Waves, Bi-Monthly Summary of Projects for Divi- 

sion 6, as of Oct. 1, 1944, 6.1 NDRC-1852. November 1944, 
pp. 31-33. Div. 6-501. 4-Ml 

35. Internal Waves, Bi-4Veekly Report U285 covering period 

from Dec. 10 to Dec. 23, 1944, NDRC 6.1-sr30-2014, UCDWR, 
Dec. 27, 1944, p. 12. Div. 6-501. 4-M2 

36. Internal Waves, Bi-Weekly Report U297 covering period 

from Jan. 21 to Feb. 3, 1945, NDRC 6.1-sr30-2025, Feb. 10, 
1945, p. 6. Div. 6-501. 4-M3 

37. Internal Waves, OSRD Bi-Monthly Summary of Projects for 

Division 6, as of Feb. 1, 1945, 6.1 NDRC-1859, March 1945, 
p. 29. Div. 6-501. 4-M4 

38. Thermal Investigations, Monthly Progress Report. April 

1945, Series I, sonar data, UCDWR MR-316-1, April 1945, 
p. 11. Div. 6-501. 4-M5 

39. Instruments for Measuring Density of Sea Water from Sub- 

niarines, WHOI, Oct. 29, 1942. Div. 6-501.322-Ml 


40. The Use of a Density Meter as an Aid to Submari7ie Diving, 

Alfred C. Redfield and Allyn C. Vine, NDRC 6.1-sr31- 
427,430, Dec. 11, 1942. Div. 6-501. 322-M2 

41. Direct Obsen>ations of Factors Affecthig Buoyancy of Sub- 

marines, Allyn C. Vine, Dean F. Bumpus, and Alfred C. 
Redfield, Aug. 11, 1943. Div. 6-501. 321-Ml 

42. Submarine Densitometers, WHOI, Nov. 9, 1943. 

Div. 6-501. 322-M3 

43. The Subtnarine Bathythermograph as an Aid in Under- 
water Operations, Nov. 22, 1943. Div. 6-501.11 -M2 

44. Examples Illustrating the Use of the Bathythermograph in 

Diving, WHOI, December 1943,. Div. 6-501. 3-M3 

45. Experiences ivith the Bathythermograph in Diving and Sug- 

gestions for its Use in Aggressive and Evasive Tactics, 
WHOI, Dec. 14, 1943. Div. 6-501. 3-Ml 

46. Pro-Submarine Warfare Research, WHOI, Apr. 13, 1944. 

Div.6-501.3-M2 

47. Tests of the Compressibility of Fifty Submarines, Dean 

F. Bumpus, Allyn C. Vine, and Alfred C. Redfield, NS-140, 
NDRC 6.1-sr31-1519, June 20, 1944. Div. 6-501.32-Ml 

48. Predicted Submarine Operating Conditions in the Ma)iito- 
u<oc Area — Lake Michigan, Sept. 1, 1944. Div. 6-501. 31-M2 

49. Reference Book for Submarine Bathythermograph Field 
Engineers, WHOI, November mi. ' Div. 6-501. 11-M7 


CON'llDENX 


CONTRACT NUMBERS, CONTRACTORS, AND SUBJECT OF CONTRACTS 


Contract 

X umber 

Name and Address 
of Cojitractor 

Subject 

OEMsi-31 

\VoocIs Hole Oceanographic Institution 
Woods Hole, Mass. 

Studies and experimental investigations in connection 
with the structure of the superficial layer of the 
ocean and its effects on the transmission of sonic and 
supersonic vibrations. 

OEMsr-20 

The Trustees of Columbia University 
in the City of New York 

New York, N. Y, 

Studies and experimental investigations in connection 
with and for the development of equipment and 
methods pertaining to submarine warfare. 

OEMsr-1131 

The Trustees of Columhia University 
in the City of New York 

New York, N, Y. 

Conduct studies and investigations in connection with 
the evaluation of the applicability of data, methods, 
devices, and systems pertaining to submarine and 
subsurface warfare. 

OEMsr-30 

The Regents of the University of 

California 

Berkeley, California 

Maintain and operate certain laboratories and conduct 
studies and experimental investigations in connec- 
tion with sidjinarine and subsurface warfare. 



79 


SERVICE PROJECT NUMBERS 


The projects listed below were transmitted to the Executive Secretary, 
National Defense Research Committee, NDRC, from the War or Navy 
Department through either the War Department Liaison Office for the 
NDRC or the Office of Research and Inventions (formerly the Coordi- 
nator of Research and Development), Navy Department. 


Service Project Numbers 


Subject 


NS-140 

Ext. 


Acoustic properties of the sea bottom 


NS-308 


NS-140 


Range as function of oceanographic factors 

Sonar-surface and submarine Bathythermograph instruction program 


80 



DECLASSIFIED 
By authority Secretary of 




INDEX 




OCI lb 1960 


I'he subject indexes of all STR volumes are combined in a mast^irind^ prb^tecij ip ^ separate volum^ 
For access to the index volume consult the Army or Navy Agency listed on the reverse oi_the half-title page. 

LIBEARY OF CONGKSS3 


Air pockets in stdmiarine tanks, buoy- 
ancy effects, 22 

Balancing, submarine, 46, 48 
Ballast, submarine; adjustments in div- 
ing, 4, 13 

effect of temperature on buoyancy, 45 
Bathythermograph; accuracy, 31, 32 
description, 25 
isoballast lines, 27 
rules for use in diving, 35, 48 
tactical submarine uses, 55-58 
Buoyancy, sidjinarine; changes during 
sid)mergence, 39 

conditions for stable buoyancy, 46 
effect of air pockets in tanks, 22 
effect of density gradients, 25-38 
effect of depth, 12 
effect of planing forces, 51-54 
resubmergence problems, 72-74 
temperature changes, 41, 45 
Buoyancy charts, sidmiarine, 61, 64-67 

Center of forward resistance, sid)marine, 
52 

Charts; density layer, 61, 66 
ocean currents, 61-63 
sonar range, 61, 68-71 
submarine buoyancy, 61, 64-67 
Coastal density gradients in ocean, 5 
Compression, submarine; compression 
coefficient, 16, 17 
effect of air pockets, 21-22 
experimental data, 19 
method of measurement, 17 
permanent set, 40 
Compression of sea water, 16 
Cooling of submarines during submer- 
gence, 41 

CTB bathythermograph, 25 
Current charts, ocean, 61-63 
CXJC bathythermograph, 2, 37 

Density gradients; effect of salinity, 8, 
1 1. 31, .33 


effect of temperature, 3-8, 10, 14 
effect on buoyancy, 14, 25^38, 46-50 
effect on submarine tactics, 56-57 
measurement by bathythermograph, 
25-38, 55-58 

Density layer charts, 61, 66 
Depth control of submarines in motion, 
53 

Diving, submarine; adjustments of bal- 
last, 4, 13, 18, 32,41 
bathythermograph rules, 35, 48 
resubmergence, 72-74 
“Diving rule,” submarine, 16 

Fuel oil temperature, effect on stability 
of sidjmarine, 42, 48 

Hull compression, submarine, 17-22, 40 
Hydrometers, marine, 18 

Internal waves in the ocean, 1 1, 57 
Isoballast bathythermograph lines, 27 
Isoballast conditions, submarine, 13 
Isothermal layers in the ocean, 5 

Leakage in submarines, 19 

Negative ocean density gradients, 4 
Negative ocean temperature gradients, 
6-8 

Net buoyancy, 12 
Neutral buoyancy, 12 

Ocean column stability, 5 
OCN bathythermograph, 26 
OCO bathythermograph, 26 

Plane angle, optimum submarine, 53 
Planing forces on submarine, 51-54 
Positive ocean temperature gradients, 10 
Propeller thrust, submarine, 52 
Range charts, sonar, 61, 68-71 
Resistance center, sid)marine, 52 


Resubmergence, submarine, 72-74 

Sailing directions, submarine, 59-71 
Salinity gradients of the ocean; effect on 
bathythermograph, 31, 33 
effect on density, 8, 14 
effect on submarine buoyancy, 3, 31 
Salinity-corrected buoyancy recorder 
(CXJC), 37 

Seasonal thermocline, 5 
Sinking rate of unbalanced submarine, 
49 

“Soaking up,” submarine, 39 
Sonar range charts, 61, 68-71 
Sound velocity recorder, underwater, 37 
Stability of ocean column, 5 
Stable buoyancy, submarine, 46 
Stop trim of submarine, 13 
Sidjinarine sailing directions, 59-71 
Submarines; buoyancy changes during 
submergence, 39-45 
buoyancy prediction, 25-38 
compression, 17-24 
diving principles, 1-2 
planing forces, 51-54 
resubmergence problems, 72-74 
stable buoyancy, 46-50 
trim adjustments, 12-13 
Submergence; see Buoyancy, submarine; 
Diving, submarine 

Tactical uses of submarine bathythermo- 
graph, 55-58 

Temperature gradients in ocean, 5-11, 
25 

Temperature— buoyancy curve, submar- 
ine, 15, 41,45 

temperature— density curve, sea water, 
15 

Thermocline, 6 

Trim adjustment of submarine, 12-13, 
24 

Unbalanced submarines, sinking rate, 49 
Ujiderwater climate, 61 


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D ECLASSIFIED 
By authority Secretary of 

01 la 1960 

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LIBRARY OF CONGRESS 


'all c ..assification 

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